£EPA
United States
Environmental Protection
Agency
Air And Radiation
(6603J)
PB94-205804
EPA402-R-94-012
June 1994
A Technical Guide To
Ground-Water Model Selection
At Sites Contaminated With
Radioactive Substances
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PB 94-205804
EPA402-R-94-012
June 1994
A TECHNICAL GUIDE TO
GROUND-WATER MODEL SELECTION
AT SITES CONTAMINATED WITH
RADIOACTIVE SUBSTANCES
A Cooperative Effort By
Office of Radiation and Indoor Air
Office of Solid Waste and Emergency Response
U.S. Environmental Protection Agency
Washington, D.C. 20460
Office of Environmental Restoration
U.S. Department of Energy
Washington, D.C. 20585
Office of Nuclear Material Safety and Safeguards
Nuclear Regulatory Commission
Washington, D.C. 20555
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PREFACE
A joint program is underway between the EPA Offices of Radiation and Indoor Air (ORIA) and
Solid Waste and Emergency Response (OSWER), the DOE Office of Environmental Restoration
and Waste Management (EM), and the NRC Office of Nuclear Material Safety and Safeguards
(NMSS). The purpose of the program is to promote the appropriate and consistent use of
mathematical models in the remediation and restoration process at sites containing, or
contaminated with, radioactive materials. This report is one of a series of reports designed to
accomplish this objective. Other reports completed under this program have identified the models
in actual use at NPL sites and facilities licensed under RCRA, and at DOE sites and NRC sites
undergoing decontamination and decommissioning (D&D), as well as the role of modeling and
modeling needs in each phase of the remedial investigation. This report specifically addresses the
selection of ground-water flow and contaminant transport models and is intended to be used by
hydrogeologists and geoscientists responsibile for identifying and selecting ground-water flow and
contaminant transport models for use at sites containing radioactive materials.
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ACKNOWLEDGMENTS
This project is coordinated by the Office of Radiation and Indoor Air, U.S. Environmental
Protection Agency, Washington, D.C., and jointly funded by the following organizations:
EPA Office of Radiation and Indoor Air (ORIA)
EPA Office of Solid Waste and Emergency Response (OSWER)
DOE Office of Environmental Restoration and Waste Management (EM)
NRC Office of Nuclear Material Safety and Safeguards (NMSS)
The project Steering Committee for this effort includes:
EPA
Beverly Irla, EPA/ORIA Project Officer
Ronald Wilhelm, EPA/ORIA
Kung-Wei Yeh, EPA/ORIA
Loren Henning, EPA/OSWER
DOE
Paul Beam, DOE/EM
NRC
Harvey Spiro, NRC/NMSS
Consultants and Contractors
John Mauro, S. Cohen & Associates, Inc.
David Back, HydroGeoLogic, Inc.*
Paul Moskowitz, Brookhaven National Laboratory
Richard Pardi, Brookhaven National Laboratory
James Rumbaugh, Geraghty & Miller, Inc.
*principal author
We acknowledge the technical support and cooperation provided by these organizations and
individuals. We also thank all reviewers for their valuable observations and comments.
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CONTENTS
Page
Preface i
Acknowledgments ii
Summary S-l
1 Introduction 1-1
1.1 Background - Purpose and Scope of the Joint EPA/DOE/NRC Program 1-1
1.2 Purpose and Scope of this Report 1-3
1.3 Principal Sources of Information 1-4
1.4 Key Terms 1-4
1.5 Organization of the Report 1-5
2 Modeling Decisions Facing the Site Remediation Manager 2-1
2.1 Is Ground Water a Potentially Important Exposure Pathway? 2-1
2.2 Reasons for Modeling 2-3
2.3 Planning for Modeling 2-3
2.3.1 Identifying Modeling Needs 2-3
2.3.2 Sources of Assistance 2-7
2.3.2.1 Branches and Divisions Within Agencies 2-7
2.3.2.2 Electronic Media 2-7
3 Constructing and Refining the Conceptual Model of the Site 3-1
3.1 Basic Questions that Will Need to be Answered 3-2
3.2 Components of the Conceptual Model for the Ground-water Pathways 3-2
3.2.1 Contaminant/Waste Characteristics 3-2
3.2.2 Environmental Characteristics 3-3
3.2.3 Land Use and Demography 3-5
4 Code Selection - Recognizing Important Model Capabilities 4-1
4.1 Introduction 4-1
4.2 General Considerations - Code Selection During Each Phase in the Remedial Process 4-1
4.2.1 Scoping 4-3
4.2.1.1 Conservative Approximations 4-3
4.2.1.2 Steady-State Solutions 4-5
4.2.1.3 Restricted Dimensionality 4-5
4.2.1.4 Uncomplicated Boundary and Uniform Initial Conditions 4-7
4.2.1.5 Simplified Flow and Transport Processes 4-8
4.2.1.6 Uniform Properties 4-8
in
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CONTENTS (Continued)
Page
4.2.2 Site Characterization 4-9
4.2.2.1 Site-Specific Approximations 4-10
4.2.2.2 Steady-State Flow/Transient Transport 4-10
4.2.2.3 Multi-Dimensional 4-11
4.2.2.4 Constant Boundary and Non-uniform Initial Conditions 4-12
4.2.2.5 Complex Flow and Transport Processes 4-13
4.2.2.6 System Heterogeneity 4-14
4.2.3 Remedial Phase 4-14
4.2.3.1 Remedial Action Specific 4-15
4.2.3.2 Transient Solutions 4-18
4.2.3.3 Multi-Dimensional 4-18
4.2.3.4 Transient Boundary and Non-Uniform Initial Conditions 4-18
4.2.3.5 Specialized Flow and Transport Processes 4-19
4.2.3.6 System Heterogeneity 4-20
4.3 Specific Considerations 4-20
4.3.1 Site-Related Characteristics 4-23
4.3.1.1 Source Characteristics 4-23
4.3.1.2 Aquifer and Soil/Rock Characteristics 4-27
4.3.1.3 Transport and Fate Processes 4-36
4.3.1.4 Multiphase Fluid Conditions 4-41
4.3.1.5 Flow Conditions 4-42
4.3.1.6 Time Dependence 4-43
4.3.2 Code-Related Characteristics 4-43
4.3.2.1 Geometry 4-44
4.3.2.2 Source Code Availability 4-45
4.3.2.3 Code Testing and Processing 4-45
4.3.2.4 Model Output 4-47
4.4 Modeling Dilemmas 4-47
5 The Code Selection Process 5-1
5.1 Overview of the Code Review and Selection Process 5-1
5.2 Evaluation Criteria 5-5
5.2.1 Administrative Data 5-5
5.2.2 Criteria Based on Phase in the Remedial Process 5-7
5.2.3 Criteria Based on Waste and Site Characteristics 5-7
5.2.4 Criteria Based on Code Characteristics 5-10
References R-l
Bibliography B-l
IV
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CONTENTS (Continued)
Page
Appendices
A Glossary A-l
B Ground-water Modeling Resources B-l
C Solution Methodology C-l
D Code Attribute Tables D-l
E Index E-l
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FIGURES
Number Page
1-1 Exposure Pathways 1-1
3-1 Example Conceptual Model 3-1
4-1 One-Dimensional Representation of Conceptual Model 4-5
4-2 Two-Dimensional Cross-Sectional Representation of Unsaturated Zone in
Conceptual Model 4-6
4-3 Two-Dimensional Areal Representation of Saturated Zone Conceptual Model 4-6
4-4 Three-Dimensional Representation of Conceptual Model 4-6
4-5 Typical System Boundary Conditions 4-7
4-6 Water Table and Confined Aquifers 4-28
4-7 Perched Water 4-31
4-8 Macropores and Fractures 4-32
4-9 Hydrodynamic Dispersion 4-38
4-10 Matrix Dispersion 4-39
5-1 Code Selection Review Process 5-3
5-2 General Classification of Selection Criteria 5-6
5-3 Physical, Chemical, and Temporal Site-Related Selection Criteria 5-9
5-4 Source Code Availability and History of Use Selection Criteria 5-11
5-5 Quality Assurance Selection Criteria 5-12
5-6 Hardware Requirements Selection Criteria 5-17
5-7 Mathematical Solution Methodology Acceptance Criteria 5-18
5-8 Code Output Selection Criteria 5-19
5-9 Code Dimensionality Selection Criteria 5-21
VI
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TABLES
Number Page
2-1 Matrix of Reasons for Modeling 2-4
4-1 General Modeling Approach as a Function of Project Phase 4-2
4-2 Questions Pertinent to Model Selection 4-21
4-3 Site-Related Features of Ground-Water Flow and Transport Codes 4-24
4-4 Code-Related Features of Ground-Water Flow and Transport Codes 4-25
5-1 Model Selection Criteria 5-4
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SUMMARY
A TECHNICAL GUIDE TO GROUND-WATER MODEL SELECTION
AT SITES CONTAMINATED WITH RADIOACTIVE SUBSTANCES
S.I INTRODUCTION
A joint program is underway between the
Environmental Protection Agency (EPA) Offices of
Radiation and Indoor Air (ORIA) and Solid Waste and
Emergency Response (OSWER), the Department of
Energy (DOE) Office of Environmental Restoration
and Waste Management (EM), and the Nuclear
Regulatory Commission (NRC) Office of Nuclear
Material Safety and Safeguards (NMSS). The purpose
of the program is to promote the appropriate and
consistent use of mathematical models in the
remediationandrestorationprocess at sites containing,
or contaminated with, radioactive materials. This
report, which is one of a series of reports designed to
accomplish this objective, specifically addresses the
selection of ground-water flow and contaminant
transport models. It is intended to be used by
hydrogeologists and geoscientists responsible for
identifying and selecting ground-water flow and
contaminant transport models for use at sites
containing or contaminated with radioactive materials.
Previous reports in this series have determined that the
types of models and the processes that require
modeling during the remedial process depend on a
combination of the following five factors:
1. reasons for modeling,
2. contaminant/waste characteristics,
3. site environmental characteristics,
4. site land use and demography, and
5. phase of the remedial process.
This report describes and provides a rationale for the
methods for selecting ground-water flow and
contaminant transport models and computer codes that
meet the modeling needs at sites containing, or
contaminated with, radioactive materials. The
selection process is described in terms of the various
site characteristics and processes requiring modeling
and the availability, reliability, and useability of the
computer codes that meet the modeling needs.
Though this report is limited to a discussion of the
model selection process, the proper application of the
selected codes is as important, if not more important,
than code selection. A code, no matter how well suited
to a particular application, could give erroneous and
highly misleading results if used improperly or with
incomplete or erroneous input data. Conversely, even
a code with very limited capabilities, or a code used at
a site which has not been well characterized, can give
very useful results if used intelligently and with a full
appreciation of the limitations of the code and the
input data.
It was not possible, within the scope of this report, to
address computer code applications, quality control,
and the presentation and interpretation of modeling
results. Future reports to be prepared under this
program will address these important topics.
The report is divided into five sections. Following this
introduction, Section 2 presents an overview of the
types of ground-water modeling decisions facing the
site remediation manager. This section is designed to
help the site manager and/or earth scientists to
determine the role of, and need for, modeling in
support of remedial decision making.
Section 3 addresses the construction of a conceptual
model of a site and how it is used in the initial
planning and scoping phases of a site remediation,
especially as it pertains to the selection and use of
ground-water flow and contaminant transport codes.
Section 4 describes the various site characteristics and
ground-water flow and contaminant transport
processes that may need to be explicitly modeled. The
purpose of this section is to help the earth scientists
recognize the conditions under which specific code
features and capabilities are needed to support
remedial decision making during each phase in the site
remediation process.
Section 5 describes the computer code review and
evaluation process for screening and selecting the
computer codes that are best suited to meet site-specific
modeling needs.
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S.2 MODELING QUESTIONS FACING
SITE REMEDIATION MANAGER
THE
A review of current regulations and guidelines
pertaining to the remediation of sites on the National
Priorities List (NPL) and in the NRC's Sites
Decommissioning Management Program (SDMP)
reveals that fate and effects modeling is not explicitly
required. However, in order to make informed and
defensible remedial decisions, ground-water flow and
contaminant transport modeling can be useful and is
often necessary.
S.2.1 When is Ground-Water Modeling
Needed?
The first questions that a site remediation manager
will need to answer regarding ground-water modeling
include: Is ground-water modeling needed, and how
will modeling aid in the remedial decision making
process?
The ground-water pathway may be considered a
potentially significant exposure pathway if (1) the
radionuclide concentrations in the ground water
exceed the levels acceptable to the cognizant regulatory
authorities or (2) the contamination at the site could
eventually cause the radionuclide concentrations in
ground water to exceed the applicable criteria. On this
basis, if the measured concentrations of radionuclides
in ground water downgradient from the site, or in
leachate at the site, exceed the applicable criteria, and
the ground water in the vicinity of the site is being
used, or has the potential to be used, as a source of
drinking water, it is likely that ground-water modeling
will be useful, if not necessary, in support of remedial
decision making at the site.
The "applicable criteria" are ill-defined at this time
because both NRC and EPA are engaged in
rulemaking activities intended to define the criteria.
However, in the interim, the drinking-water standards
set forth in 40 CFR 141 should guide remedial
decision making. For example, 40 CFR 141 has been
cited as an applicable or relevant and appropriate
regulation (ARAR) in establishing the remediation
goals at most of the approximately 50 sites
contaminated with radioactive material that are
currently on the National Priorities List.
At some sites, information may not be available
regarding the levels of radionuclide contamination in
ground water or leachate. Alternatively, radionuclide
measurements may have been made, but yield
inconclusive results. Under these conditions, the
radionuclide concentrations in leachate and ground
water can be estimated based on knowledge of the
radionuclide concentrations in the soil or the waste at
the site and empirically determined partition factors.
Partition factors relate a given concentration of a
contaminant in the waste or the soil to that in the
leachate or ground water.
If the product of the radionuclide concentrations in the
waste or contaminated soil with the appropriate
partition factors results in radionuclide concentrations
in leachate or ground water in excess of the applicable
criteria, it may be concluded that the radionuclide
concentrations in ground water in the vicinity of the
site could exceed the applicable criteria. Though it is
not necessarily always the case, if the measured or
derived concentrations of radionuclides in ground
water exceed the applicable criteria, it is likely that
ground-water modeling will serve a useful role in
support of remedial decision making at the site.
S.2.2 When is Modeling Not Needed or
Inappropriate?
It is important to be able to recognize the
circumstances under which modeling would be
ineffective and should probably not be performed.
There are three general scenarios in which modeling
would be of limited value. These are:
1. Presumptive remedies can be readily
identified,
2. Decision making is based on highly
conservative assumptions, and/or
3. The site is too complex to model
realistically.
The first case arises in situations where a presumptive
remedy is apparent; that is, where the remedy is
obvious based on regulatory requirements or previous
experience, and there is a high level of assurance that
the site is well understood and the presumptive remedy
will be effective. An example would be conditions that
obviously require excavation or removal of the
contaminant source.
The second case is based on the assumption that
decision making can proceed based on conservative
estimates of the behavior and impacts of contaminants
at the site rather than detailed modeling. This strategy
S-2
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could be used in the initial scoping, site
characterization, or remedial phase of the
investigation. For example, a conservative approach
to the risk assessment would be to assume that the
contaminant concentrations at the receptor(s) are
identical to the higher concentrations detected at the
contaminant source. Thus, the need for modeling to
determine the effects of dilution and attenuation on
contaminant concentrations is removed.
The third case involves sites where modeling would be
helpful in supporting remedial decision making, but
the complexity of the site precludes reliable modeling.
These complexities could be associated with the
contaminant source, flow and transport processes, or
characteristics of the wastes and contaminants. For
example, the contaminant source may be so poorly
defined in terms of areal extent, release history, and
composition that it cannot be reliably defined and little
would be gained from flow and transport modeling.
Complex flow and contaminant transport processes
present another difficulty in that user-friendly
computer codes currently do not exist that
accommodate a number of these processes, which
include: turbulent ground-water flow, facilitated
transport (e.g., due to the formation of colloids), and
flow and transport through a fractured unsaturated
zone.
The availability of computer codes is also an issue
when characteristics of the contaminants are typified
by complex geochemical reactions, such as phase
transformations and non-linear sorption processes.
Currently, ground-water flow and contaminant
transport codes that provide credible mathematical
descriptions of the more complex geochemical
processes have not been developed. If modeling is not
possible because of the overall complexity of the site
characteristics, it is common for a greater emphasis to
be placed on empirical rather than predicted data.
This may involve establishing long-
term monitoring programs, which, in effect, have
objectives similar to those of ground-water modeling.
S.2.3 What Role Will Ground-Water Modeling
Play in Support of Remedial
Decision Making?
Once it is determined that the ground-water exposure
pathway is potentially important, ground-water flow
and transport modeling can have a wide range of uses
in support of remedial decision making. The following
are the principal reasons for modeling on a remedial
project. These applications can surface during any
phase of the remedial process. However, some of these
reasons are more likely to occur during specific phases
of a remedial project.
1. When it is not feasible to perform field
measurements; i.e.,
! Cannot get access to sampling locations
! Budget is limited
! Time is limited
2. When there is concern that downgradient locations
may become contaminated at some time in the
future; i.e.,
i
When transport times from the source of the
contamination to potential receptor locations
are long relative to the period of time the
source of the contaminant has been present.
When planning to store or dispose of waste at
a specific location and impacts can be
assessed only through the use of models.
3. When field data alone are not sufficient to
characterize fully the nature and extent of the
contamination; i.e.,
! When field sampling is limited in space and
time, and
! When field sampling results are ambiguous or
suspect.
4. When there is concern that conditions at a site
may change, thereby changing the fate and
transport of the contaminants; i.e.,
! seasonal changes in environmental conditions
! severe weather (e.g., floods)
! accidents (e.g., fires)
5. When there is concern that institutional control at
the site may be lost at some time in the future
S-3
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resulting in new exposure scenarios, or a change
in the fate and transport of the contaminants; i.e.,
! trespassers
! inadvertent intruder (construction/
agriculture)
! human intervention (drilling, excavations,
mining)
6. When remedial actions are planned and there is a
need to predict the effectiveness of alternative
remedies.
7. When there is a need to predict the time when the
concentration of specific contaminants at specific
locations will decline to acceptable levels (e.g.,
natural flushing).
8. When there is concern that at some time in the
past individuals were exposed to elevated levels of
contamination and it is desirable to reconstruct the
doses.
9. When there is concern that contaminants may be
present but below the lower limits of detection.
10. When field measurements reveal the presence of
some contaminants, and it is desirable to
determine if and when other contaminants
associated with the source may arrive, and at what
levels.
11. When field measurements reveal the presence of
contaminants and it is desirable to identify the
source or sources of the contamination.
12. When there is a need to determine the timing of
the remedy; i.e., if the remedy is delayed, is there
a potential for environmental or public health
impacts in the future?
13. When there is a need to determine remedial action
priorities.
14. When demonstrating compliance with regulatory
requirements.
15. When estimating the benefit in a cost-benefit
analysis of alternative remedies.
16. When performing a quantitative dose or risk
assessment pertaining to the protection of
remediation workers, the public, and the
environment prior to, during, and following
remedial activities.
17. When designing the site characterization program
(e.g., placement of monitor wells, determining
data needs) and identifying exposure pathways of
potential significance.
18. When there is a need to compute or predict the
concentration distribution in space and time of
daughter products from the original source of
radionuclides.
19. When there is a need to quantify the degree of
uncertainty in the anticipated behavior of the
radionuclides in the environment and the
associated doses and risks.
20. When communicating with the public on the
potential impacts of the site and the benefits of the
selected remedy.
S.2.4 What Will the Results of a Modeling
Exercise Yield?
Once the need for, and role of, modeling is identified,
it is appropriate to determine or define the form of the
results or output of the modeling exercise. In general,
the results are expressed as a concentration, such as
pCi/L in ground water at a specific location. The
derived radionuclide concentrations could also be
expressed as a function of time or as a time-averaged
value.
Some computer codes have the ability to convert the
derived radionuclide concentrations in ground water to
doses or risks to individuals exposed to the
contaminated ground water. These results are
generally expressed in units of mrem/yr or lifetime risk
of cancer for the exposed individuals.
Some computer codes can present the results in terms
of cumulative population impacts. These results are
generally expressed in terms of person-rems/yr or total
number of cancers induced per year in the exposed
population.
The specific regulatory requirements that apply to the
remedial program determine which of these "end
products" are needed. In general, these modeling
results are used to assess impacts or compliance with
S-4
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applicable regulations; however, information regarding
radionuclide flux and plume arrival times and
distributions is also used to support a broad range of
remedial decisions.
These modeling endpoints must be clearly defined,
since the type of endpoint will help to determine the
type of ground-water flow and contaminant transport
model that will support the endpoint of interest. For
example, a baseline risk assessment at a site
contaminated with radioactive material is used in
determining the annual radiation dose to an individual
drinking water obtained from a potentially
contaminated well. The endpoint in this case is the
dose to an individual expressed in units of mrem/yr.
In order to estimate this dose, it is necessary to
estimate the average concentration of radionuclides in
the well water over the course of a year. The models,
input parameters, and assumptions needed to predict
the annual average radionuclide concentration are
different than those needed to predict the time varying
concentration at a given location. The latter usually
requires much more input data and models capable of
simulating dynamic processes.
S.3 CONSTRUCTING A CONCEPTUAL
MODEL OF A SITE - THE FIRST STEP
IN THE MODEL SELECTION
PROCESS
The first step in the model selection process is the
construction of a conceptual model of the site. The
conceptual model depicts the types of waste and
contaminants, where they are located (e.g., are they
currently only in the surficial soil or have they
migrated to the underlying aquifer?), and how they are
being transported offsite (e.g., by runoff, percolation
into the ground, and transport in ground water, or
suspension or volatilization into the air and transport
by the prevailing meteorological conditions). The
conceptual model also attempts to help visualize the
direction and path followed by the contaminants, the
controlling factors that affect the contaminant
migration through the subsurface (i.e., hydrogeology,
system boundary conditions), the actual or potential
locations of the receptors, and the ways in which
receptors may be exposed, such as direct contact with
the source, ingestion of contaminated food or water, or
inhalation of airborne contaminants. As information
regarding a site accumulates, the conceptual model is
continually revised and refined.
A mathematical model translates the conceptual model
into a series of equations which simulate the fate and
effects of the contaminants as depicted in the
conceptual model at a level of accuracy that can
support remedial decision making. A computer code
is simply a tool that is used to solve the equations
which constitute the mathematical model of the site
and display the results in a manner convenient to
support remedial decision making. Accordingly, code
selection must begin with the construction of a
conceptual model of the site.
The components that make up the initial conceptual
model of the site include:
1. the waste/contaminant characteristics,
2. the site characteristics, including
hydrogeology, land use, and demography, and
3. the exposure scenarios and pathways.
S.3.1 Waste/Contaminant Characteristics
To the extent feasible, the site conceptual model should
address the following characteristics of the
waste/contaminants:
! Types and chemical composition of the
radionuclides
! Waste form and containment
! Source geometry (e.g., volume, area, depth,
homogeneity)
Within the context of ground-water modeling, these
characteristics are pertinent to modeling the source
term, i.e., the rate at which radionuclides are
mobilized from the source and enter the unsaturated
and saturated zones of a site.
S.3.2 Site Characteristics
The conceptual model of the site should begin to
address the complexity of the environmental and
hydrogeological setting. A complex setting, such as
complex lithology, a thick unsaturated zone, and/or
streams or other bodies of water on site, generally
indicates that the direction and velocity of ground-
water flow and radionuclide transport at the site cannot
be reliably simulated using simple models.
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However, even at complex sites, complex models may
not be needed. For example, if a conservative
approach is taken, where transport through the
unsaturated zone is assumed to be instantaneous, then
the complex processes associated with flow and
transport through the unsaturated zone would not need
to be modeled. Such an approach would be
appropriate at sites where the remedy is likely to be
removal of the contaminated surface and near-surface
material.
The site conceptual model will also need to identify the
locations where ground water is currently being used,
or may be used in the future, as a private or municipal
water supply. At sites with multiple user locations, an
understanding of ground-water flow in two or three
dimensions is needed in order to predict realistically
the likelihood that the contaminated plume will be
captured by the wells located at different directions,
distances, and depths relative to the sources of
contamination.
Simple ground-water flow and transport models
typically are limited to estimating the radionuclide
concentration in the plume centerline down-gradient
from the source. Accordingly, if it is assumed that the
receptors are located at the plume centerline, a simple
model may be appropriate. Such an assumption is
often appropriate even if a receptor is not currently
present at the centerline location because the results
are generally conservative. In addition, risk
assessments often postulate that a receptor could be
located directly down-gradient of the source at some
time in the future.
The need for complex models increases if there are a
number of water supplies in the vicinity of the source.
Under these circumstances, it may be necessary to
calculate the cumulative population doses and risks,
which require modeling the radionuclide
concentrations at a number of specific receptor
locations. Accordingly, off-centerline modeling which
includes dispersion may be needed.
S.3.3 Exposure Scenarios and Pathways
The conceptual model of the site will also need to
define the exposure scenarios and pathways at the site.
An exposure scenario pertains to the assumed initial
conditions or initiating events responsible for the
transport of the radionuclides and exposure of the
nearby population. Depending on the regulatory
requirements and the phase in the remedial process,
the exposure scenarios that will need to be modeled
can include any one or combination of the following:
! The no action alternative - Under this
scenario, the radiation doses and risks to
members of the public, now and in the future,
are derived assuming no action is taken to
remedy the site or protect the public from
gaining access to the site.
! Trespassers - This scenario postulates that an
individual trespasses on the site.
! Inadvertent intruder - This scenario
postulates that an individual establishes
residence at the site.
! Routine emissions - This scenario simply
assesses offsite doses and risks associated
with the normally anticipated releases from
the site. (This concept is similar to the "No
Action Alternatives," but is used within the
context of NRC licensed facilities.)
! Accidents - This scenario assesses doses and
risks associated with postulated accidental
releases from the site.
! Alternative remedies - This set of scenarios
assesses the doses and risks to workers and
the public associated with the implementation
of specific remedies and the reduction in
public doses and risks following
implementation of the remedy.
The number of scenarios that may be postulated is
virtually unlimited. Accordingly, it is necessary to
determine which scenarios reasonably bound what may
in fact occur at the site. The types of scenarios selected
for consideration influence modeling needs because
they define the receptor locations and exposure
pathways that need to be modeled.
For each scenario, an individual or group of
individuals may be exposed by a wide variety of
pathways. The principal pathways include:
! External exposure to deposited radionuclides
S-6
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! External exposures to airborne, suspended,
and resuspended radionuclides
! Inhalation exposures to airborne, suspended,
and resuspended radionuclides
! Ingestion of radionuclides in food items and
drinking water
! Ingestion of contaminated soil and sediment
! External exposures from immersion in
contaminated water
S.4 CODE SELECTION - RECOGNIZING
IMPORTANT MODEL CAPABILITIES
The greatest difficulty facing the investigator during
the code selection process is not determining which
codes have specific capabilities, but rather which
capabilities are actually required to support remedial
decision making during each remedial phase at a
specific site. This section is designed to help the
remedial manager recognize the conditions under
which specific model features and capabilities are
needed to support remedial decision making.
S.4.1 Code Selection During the Different Phases
of a Remedial Program
Successful ground-water modeling requires the
selection of a computer code that is not only consistent
with the site characteristics but also with the modeling
objectives, which are strongly dependent on the phase
of the remedial process; i.e., scoping versus site
characterization versus the selection and
implementation of a remedy. Table S-l presents an
overview of how the overall approach to modeling a
site differs as a function of the phase of the remedial
process.
The most common code selection mistakes are
selecting codes that are more sophisticated than are
appropriate for the available data or the level of the
result desired, and the application of a less
sophisticated code that does not account for the flow
and transport processes that dominate the system.
Table S-l. General Modeling Approach as a Function of Project Phase
Attributes
Accuracy
Temporal Representation of
Flow and Transport Processes
Dimensionality
Boundary and Initial
Conditions
Assumptions Regarding Flow
and Transport Processes
Lithology
Methodology
Data Requirements
Scoping
Conservative
Approximations
Steady-State Flow and
Transport Assumptions
One Dimensional
Uncomplicated
Boundary and Uniform
Initial Conditions
Simplified Flow and
Transport Processes
Homogeneous/Isotropic
Analytical
Limited
Characterization
Site-Specific
Approximations
Steady-State Flow/Transient
Transport Assumptions
1 ,2-Dimensional/Quasi-
3-dimensional
Non-Transient Boundary
and Nonuniform Initial
Conditions
Complex Flow and
Transport Processes
Heterogeneous/Ani so tropic
Semi-Analytical/Numerical
Moderate
Remediation
Remedial Action Specific
Transient Flow and
Transport Assumptions
Fully 3-Dimensional/Quasi-
3-dimensional
Transient Boundary and
Nonuniform Initial
Conditions
Specialized Flow and
Transport Processes
Heterogeneous/Ani so tropic
Numerical
Extensive
S-7
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For example, a typical question that often arises is:
should three-dimensional codes be used as opposed to
two- or one-dimensional codes? Inclusion of the third
dimension requires substantially more data than one-
and two- dimensional codes. Similar questions need to
be considered which involve the underlying
assumptions in the selection of an approach and the
physical processes which are to be addressed. If the
modeler is not practical, sophisticated codes are used
too early in the problem analysis. In other instances,
the complexity of the modeling is commensurate with
the qualifications of the modeler.
An inexperienced modeler may take an unacceptably
simplistic approach. One should begin with the
simplest code appropriate to the problem and progress
toward the more sophisticated codes until the modeling
objectives are achieved.
The remedial process is generally structured in a way
that is consistent with this philosophy; i.e., as the
investigation proceeds, additional data become
available to support more sophisticated ground-water
modeling.
The data available in the early phases of the remedial
process may limit the modeling to one or two
dimensions. In certain cases, this may be sufficient to
support remedial decision making. If the modeling
objectives cannot be met in this manner, additional
data will be needed to support the use of more complex
models.
It is generally in the later phases of the investigation
that sufficient data have been obtained to meet more
ambitious objectives through complex three-
dimensional modeling.
The necessary degree of sophistication of the modeling
effort can be evaluated in terms of both site-related
issues and objectives, as well as the qualities inherent
in the computational methods available for solving
ground-water flow and transport equations.
Modeling objectives at each stage of the remedial
investigation must be very specific and well defined
early in the project. All too often, modeling is
performed without developing a clear rationale to meet
the objectives, and only after the modeling is
completed are the weaknesses in the approach
discovered.
The modeling objectives must consider the available
data and the remedial decisions that the model results
are intended to support. The selected modeling
approach should not be driven by the data availability,
but the modeling objectives should be defined in terms
of what can be accomplished with the available data.
If the modeling objectives demand more sophisticated
models and input data, the necessary data should be
obtained.
A final consideration, true for all phases of the project,
is to select codes that have been accepted by technical
experts and used within a regulatory context.
S.4.2 The Effects of Waste/Contaminant and Site
Characteristics on Code Selection
After the conceptual model is formulated and the
modeling objectives are clearly defined, the
investigator should have a relatively good idea of the
level of sophistication that the anticipated modeling
will require. It now becomes necessary to select one or
more computer code(s) that have the attributes
necessary to mathematically describe the conceptual
model at the desired level of detail. This step in the
code selection process requires detailed analysis of the
conceptual model to determine the degree to which
specific waste/contaminant and site characteristics
need to be explicitly modeled.
The code selection process consists primarily of
determining which waste/contaminant and site charac-
teristics and flow and transport processes need to be
explicitly modeled in order to achieve the modeling
objectives. Once these are determined, the code
selection process becomes simply a matter of identi-
fying the codes that meet the defined modeling needs.
Table S-2 lists code attributes related to various
waste/contaminant and site characteristics. This table
illustrates the site-related criteria generally considered
in the identification of candidate computer codes.
The general components of the conceptual model that
need to be considered when selecting an appropriate
computer code are the following:
! Source Characteristics
! Aquifer and Soil/Rock Characteristics
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Table S-2. Site-Related Features of Ground-Water Flow and Transport Codes
Section 4. 3. 1.1
Section 4. 3. 1.2
Section 4. 3. 1.3
Section 4. 3. 1.4
Section 4. 3. 1.5
Section 4. 3. 1.6
Source Characteristics
Point Source
Line Source
Areally Distributed Source
Multiple Sources
Specified Concentration
Specified Source Rate
Time-Dependent Release
Aquifer and Soil/Rock Characteristics
Confined Aquifers
Confining Unit(s)
Water-Table Aquifers
Convertible Aquifers
Multiple Aquifers
Homogeneous
Heterogeneous
Isotropic
Anisotropic
Fractures
Macropores
Layered Soils
Fate and Transport Processes
Dispersion
Advection
Matrix Diffusion
Density -Dependent Flow and Transport
Retardation
Non-linear Sorption
Chemical Reactions/Speciation
Single Species First Order Decay
Multi-Species Transport with Chained Decay Reactions
Multiphase Fluid Conditions
Two-Phase Water/NAPL
Two-Phase Water/ Air
Three-Phase Water/NAPL/ Air
Flow Conditions
Fully Saturated
Convertible Aquifers
Variably Saturated/Non-Hysteretic
Variably Saturated/Hysteretic
Time Dependence
Steady-State
Transient
Fate and Transport Processes
Multiphase Fluid Conditions
S-9
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Each of these topics is presented as a major heading in
Table S-2. These broad subjects are further broken
down into their individual components both in Table
S-2 and in the discussion that follows.
Source Characteristics
Computer codes can accommodate the spatial
distribution of the contaminant source in a number of
ways. The most common are:
Point source, such as a waste drum or tank,
Line source, such as a trench, and
Area source, such as ponds, lagoons, or
landfills.
The determination of how the spatial distribution of
the source term should be modeled (i.e., point, line, or
area) is dependent on a number of factors, the most
important of which is the scale at which the site will be
investigated and modeled. If the region of interest is
very large, as compared to the contaminant source
area, even sizable lagoons or landfills could be
considered point sources.
The modeling objectives are also important in
determining the way in which the source term should
be modeled. For example, if simple scoping
calculations are being performed, treating the source as
a point will yield generally conservative
approximations of contaminant concentrations because
of limited dispersion. However, if more realistic
estimates of concentrations and plume geometry are
required, it will be generally necessary to simulate the
source term characteristics more accurately, especially
if the receptor is close to a relatively large source.
In addition to the geometry of the source, code
selection is determined by whether the source is to be
modeled as a continuous or time-varying release.
Computer codes can simulate the introduction of
contaminants to the ground water as an instantaneous
pulse or as a continuous release over time. A
continuous release may either be constant or vary with
time.
The need to model the source as a constant or time-
varying release primarily depends on the half-life of
the radionuclide relative to the time period of interest
and whether average impacts or time-varying impacts
of a release are of interest. In general, the simplest
calculations, which assume a continuous release, are
sufficient when determining the average annual doses
to ground-water users at sites with relatively long-lived
radionuclides.
Aquifer and Soil/Rock Characteristics
The most common site characteristics with regard to
aquifers that influence code selection include the
following:
! Confined aquifers
! Water-table (unconfined) aquifers
! Convertible aquifers
! Multiple aquifers/aquitards
! Heterogeneous aquifers
! Anisotropic aquifers
! Fractures/Macropores
! Layered soils/rocks
Recognizing when and if these processes need to be
explicitly modeled is critical to the code selection
process. There are no simple answers to these
questions. However, the following general guidance
may be helpful in making these determinations.
Confined versus Unconfined Aquifers
In most circumstances, the concern at a contaminated
site is contamination of unconfined aquifers since
sources of ground water generally become
contaminated by leachate migrating from
contaminated surface soil through an unsaturated zone
of varying thicknesses to an aquifer. However,
confined aquifers could be of concern at sites where
contaminants were disposed in injection wells and
layered sites with "leaky aquitards."
Multiple Aquifers/Aquitards
Computer codes have been developed that have the
ability to simulate either single or multiple
S-10
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hydrogeologic layers. Generally, a single-layer code is
used if the bulk of the contamination is confined to
that layer or if the difference in the flow and transport
parameters between the various layers is not significant
enough to warrant the incorporation of various layers.
It generally does not make much sense to model
discrete layers if estimated parameter values,
separating different layers, fall within probable error
ranges for the parameters of interest. Furthermore,
unless the discrete hydrogeologic units are continuous
over the majority of the flow path, it is often possible
and preferable to model the system as one layer using
average flow and transport properties.
Layered Soil/Rocks in the Unsaturated Zone
Rarely would soils and rocks within the unsaturated
zone not exhibit some form of natural layering. The
first consideration as to how this natural layering
should be treated in the modeling analysis is related to
whether the various soil layers have significantly
different flow and transport properties. If these
properties do not vary significantly from layer to layer,
there would be little need for the code to have
multiple-layer capability. On the other hand, if the
layers have distinctive properties that could affect flow
and transport, a decision needs to be made about how
best to achieve the modeling objectives; i.e., should
each layer be discretely treated or should all of the
layers be combined into a single layer.
Macropores/Fractures
Modeling flow through the unsaturated zone is based
on the assumption that the soil is a continuous
unsaturated solid matrix that holds water within the
pores. Actual soil, however, has a number of cracks,
root holes, animal burrows, etc., where the physical
properties differ enormously from the surrounding soil
matrix. Under appropriate conditions, these flow
channels have the capacity to carry water at velocities
and concentrations that greatly exceed those in the
surrounding matrix. Accordingly, it is critical to
determine whether ground-water flow and contaminant
transport at a site is dominated by macropores and
fractures because this factor could determine whether
a contaminant can reach the saturated zone almost
immediately versus a transit time on the order of
hundreds to thousands of years. This issue is
especially important for radionuclides where
radioactive decay in transit in the unsaturated zone
could virtually eliminate the concern over ground-
water contamination.
Anisotropic/Isotropic
In a porous medium made of spheres of the same
diameter packed uniformly, the geometry of the voids
is the same in all directions. Thus, the intrinsic
permeability of the unit is the same in all directions,
and the unit is said to be isotropic. On the other hand,
if the geometry of the voids is not uniform, and the
physical properties of the medium are dependent on
direction, the medium is said to be anisotropic.
In most sedimentary environments, clays and silts are
deposited as horizontal layers. This preferential
orientation of the mineral particles allows the
horizontal velocity of the contaminants to greatly
exceed those in the vertical direction. If anisotropy is
not taken into account for the modeling analysis, the
contaminants will be predicted to be more dispersed in
the vertical direction than would probably be occurring
in the real world. The result could be an under-
prediction of the concentration of the contaminant in
the centerline and an over-prediction of the
contaminant concentration off-center in the vertical
direction.
Homogeneous/Heterogeneous
A homogeneous unit is one that has the same
properties at all locations. For example, for a
sandstone, this would mean that the grain-size
distribution, porosity, degree of cementation, and
thickness vary only within small limits. As a result,
the velocity and the volume of ground water would be
about the same at all locations. In heterogeneous
formations, hydraulic properties change spatially.
For example, if it is expected that the aquifer thickness
will vary significantly (e.g., greater than ten percent),
a computer code capable of simulating variable
thicknesses is needed. If a code does not properly
simulate the aquifer thicknesses, the contaminant
velocities will be too large in areas where the
simulated aquifer is thinner than the true aquifer
thickness and too small in those regions that have too
great a simulated thickness.
The ability to simulate aquifer heterogeneities may also
be important during the remedial design phase of the
investigation. If engineered barriers of low
S-ll
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permeability are evaluated as potential remedial
options, it would be necessary to determine their
overall effectiveness. In this scenario, it would not
only be important to select a computer code that has
the capability to simulate highly variable ground-water
velocities but also to ensure that the sharp changes in
ground-watervelocities do not cause instabilities in the
mathematical solutions.
Fate and Transport Processes
The transport of radionuclides will be affected by
various geochemical and mechanical processes.
Among the geochemical processes are adsorption on
mineral surfaces and processes leading to precipi-
tation. These processes are important primarily
because they reduce the velocity of the radionuclides
relative to the ground water (i.e., retardation), which
increases the transit time to receptor locations and
results in additional radioactive decay in transit.
The following summarizes the primary processes that
affect the mobility and concentrations of radionuclides
being transported by ground water, including:
! Advection
! Dispersion
! Matrix Diffusion
! Retardation
! Radioactive Decay
Advection
The process by which solutes are transported by the
bulk movement of water is known as advection. The
amount of solute that is being transported is a function
of its concentration in the ground water and the flow
rate of the ground water.
Computer codes that consider only advection are ideal
for designing remedial systems (e.g., pump and treat)
because the model output is in the form of solute
pathlines (i.e., particle tracks) which delineate the
actual paths that a contaminant would follow.
Therefore, capture zones created by pumping wells are
based solely on hydraulic gradients and are not subject
to typical problems that occur when solving
contaminant transport equations that include
dispersion and diffusion.
Advective codes are also excellent in the remedial
design stage for determining the number and
placement of extraction or injection wells and in
evaluating the effect that low permeability barriers may
have on the flow system. They also tend to yield more
accurate travel-time determinations of unretarded
contaminants because the solution techniques are
inherently more stable, and numerical oscillations,
which artificially advance the contaminant front, are
minimized. Another important advantage of advective
codes is that the output (i.e., particle tracks) are a very
effective means of ensuring that ground-water
gradients, both vertical and horizontal, are consistent
with the conceptual model.
Notwithstanding these advantages, advective codes
have some drawbacks. The most significant of these
are their inability to address adsorption and matrix
diffusion. As discussed below, these processes can
determine the length of time that a pump and treat
system must operate before clean-up goals will be met.
Without the ability to evaluate the effects that
adsorption and diffusion may have on solute transport,
it would be very difficult to estimate remediation times.
A second potential problem with advection-based
codes is that dispersion will tend to spread
contaminants over a much wider area than would be
predicted if only advective processes are considered,
thereby underestimating the extent of contamination.
However, because dilution due to dispersion is under-
accounted for, unrealistically high peak concentrations
are generally obtained, which may be appropriate if
conservative estimates are desired. An additional
disadvantage is that pure advection-based problems
result in hyperbolic instead of parabolic equations
which cannot be solved numerically due to severe grid
and time-step constraints.
Hydrodynamic Dispersion
In addition to advective transport, the transport of
contaminants in porous media is also influenced by
dispersion and diffusion, which tend to spread the
solute out from the path that it would be expected to
follow if transported only by advection. This
spreading of the contamination over an ever-increasing
area, called hydrodynamic dispersion, has two
components: mechanical dispersion and diffusion.
Hydrodynamic dispersion causes dilution of the solute
and occurs because of spatial variations in ground-
water flow velocities and mechanical mixing during
fluid advection. Molecular diffusion, the other
component of hydrodynamic dispersion, is due to the
S-12
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thermal-kinetic energy of solute particles and also
contributes to the dispersion process. Diffusion in
solutions is the process whereby ionic or molecular
constituents move in the direction of their
concentration gradient. Thus, if hydrodynamic
dispersion is factored into the solute transport
processes, ground-water contamination will cover a
much larger region than in the case of pure advection,
with a corresponding reduction in the maximum
concentrations of the contaminant.
Matrix Diffusion
The diffusion of radionuclides from water moving
within fractures, or coarse-grained material, into the
rock matrix or finer grained clays can be an important
means of slowing the transport of the dissolved
radionuclides, particularly for non-sorbing or low-
sorbing soluble species.
Matrix diffusion is frequently insignificant and is often
neglected in many of the contaminant-transport codes.
However, a number of potential problems arise when
matrix diffusion is ignored and contaminant velocities
are based solely on advective-dispersive principles.
For example, ground-water pump and treat
remediation systems work on the premise that a
capture zone is created by the pumping well and all of
the contaminants within the capture zone will
eventually flow to the well. The rate at which the
contaminants flow to the well may, however, be very
dependent on the degree to which the contaminants
have diffused into the fine grained matrix (e.g., clays).
This is because the rate at which they will diffuse back
out of the fine grained materials may be strongly
controlled by concentration gradients, rather than the
hydraulic gradient created by the pumping well.
Therefore, matrix diffusion can significantly retard the
movement of contaminants, and, if the computer code
does not explicitly account for this process, the overall
effectiveness of the remediation system (i.e., clean-up
times) could be grossly underestimated. Matrix
diffusion processes can also lead to erroneous model
predictions in the determination of radionuclide travel
times, peak concentrations, and flushing volumes.
In general, matrix diffusion can be a potentially
important process in silty/sandy soil which contains
layers of clay or fractured rock. Through the process
of matrix diffusion, the clay and rock can serve as
reservoirs of contaminants that slowly leak back into
the ground water over a long period of time.
Retardation
In addition to the physical processes, the transport of
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radionuclides is affected by chemical processes.
most important include:
! Sorption ~ the sorption of chemical species
on mineral surfaces, such as ion exchange,
chemisorption, van der Waals attraction, etc.,
or ion exchange within the crystal structure.
! Ion exchange phenomena ~ that type of
sorption restricted to interactions between
ionic contaminants and geologic materials
with charged surfaces which can retard the
migration of radionuclides.
A wide range of complex geochemical reactions can
affect the transport of radionuclides, many of which
are poorly understood and are primarily research
topics. From a practical view, the important aspect is
the removal of solute from solution, irrespective of the
process. For this reason, most computer codes simply
lump all of the cumulative effects of the geochemical
processes into a single term (i.e., distribution
coefficient) which describes the degree to which the
radionuclide is retarded relative to the ground water.
Thus, the distribution coefficient relates the
radionuclide concentration in solution to
concentrations adsorbed to the soil. Because the
distribution coefficient is strongly affected by site-
specific conditions, it is frequently obtained from batch
or column studies in which aliquots of the solute, in
varying concentrations, are well mixed with
representative solids from the site, and the amount of
solute removed from the water to the solid is
determined.
From the perspective of model selection, virtually all
computer codes explicitly address retardation through
the use of retardation factors, which are derived from
the distribution coefficient. The primary concern is
that the retardation factors are appropriate for the site
and conditions under consideration. Spacial and
temporal changes in pH and the presence of chelating
agents could invalidate the retardation factors selected
for use at a site.
Radioactive Decay
Radionuclides decay to either radioactively stable or
unstable decay products. For some radionuclides,
S-13
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several decay products may be produced before the
parent species decays to a stable element. These
radioactive decay products may present a potentially
greater adverse health risk than the parent.
Accounting for the chain-decay process is particularly
important for predicting the potential impacts of
naturally occurring radionuclides, such as uranium and
thorium, and transuranics. In considering this process
over the transport path of radionuclides, one transport
equation must be written for each original species and
each decay product to yield the concentration of each
radionuclide (original species and decay products) at
points of interest along the flow path in order to
estimate total radiological exposures. However, not all
computer codes that simulate radioactive decay allow
for ingrowth of the decay products, which may not
cause a problem if the half-lives of the parent and
daughters are very long (i.e., it takes a long time for
the daughter products to grow in) or if the decay
products are of little interest.
Multiphase Fluid Conditions
The movement of contaminants that are immiscible in
water (i.e., non-aqueous phase liquids - NAPL)
through the unsaturated zone and below the water table
results in systems that have multiple phases (i.e., air,
water, NAPL). This coexistence of multiple phases
can be an important facet in many contaminant-
transport analyses. However, only the water and the
vapor phase are generally of concern when evaluating
the transport of radionuclides. A limited number of
radionuclides can form volatile species that are capable
of being transported in a moving vapor or gas. Among
these are tritium, carbon-14, radon-220/222, and
iodine-129. Accordingly, if these radionuclides are
present, vapor phase transport may need to be
explicitly considered.
S.5 THE CODE SELECTION PROCESS
Given that an investigator understands the various
waste/contaminant and site characteristics that need to
be modeled in order to meet specific modeling
objectives, there will oftenbe several suitable computer
codes that could potentially be chosen from a large
number of published codes presented in the scientific
literature. Ideally, each candidate code should be
evaluated in detail to identify the one most appropriate
for the particular site and modeling objectives.
However, the resources to complete a detailed study are
seldom available, and usually only one to two codes are
selected based upon a cursory review of code
capabilities and the experience of the modeler.
Regardless of whether a detailed or more cursory
review is performed, it is important for the reviewer/
investigator to be cognizant of the following factors
and how they will affect code selection:
1. Code Capabilities consistent with:
User needs
Modeling objectives
Site characteristics
Contaminant characteristics
Quality and quantity of data
2. Code Testing
Documentation
Verification
Validation
3. History of Use Acceptance
The first aspect of the review concentrates on the
appropriateness of the particular code to meet the
modeling needs of the project. The reviewer must also
determine whether the data requirements of the code
are consistent with the quantity and quality of data
available from the site. Next, the review must
determine whether the code has been properly tested
for its intended use. Finally, the code should have
some history of use on similar projects, be generally
accepted within the modeling community, and readily
available to the public.
Evaluating a code in each of the three categories can
be a significant undertaking, especially with respect to
code testing. Theoretically, the reviewer should obtain
a copy of the computer code, learn to use the code,
select a set of verification problems with known
answers, and compare the results of the model to the
benchmark problems. This task is complicated, largely
because no standard set of benchmark problems exists
and the mathematical formulation for each process
described within the code has to be verified through
the benchmarking process. It is recommended,
primarily for this reason, that the codes selected
already be widely tested and accepted. Model
validation, which involves checking the model
predictions against independent field investigations
designed specifically to test the accuracy of the model,
would almost never be practical during the code
evaluation and selection process.
S-14
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The model evaluation process involves the following
steps:
1. Contact the author of the code and obtain the
following:
- Documentation and other model-related
publications
- List of users
- Information related to code testing
2. Read all publications related to the model,
including documentation, technical papers, and
testing reports.
3. Contact code users to find out their opinions.
4. Complete the written evaluation using the criteria
shown in Table S-3.
Much of the information needed for a thorough
evaluation can be obtained from the author or
distributor of the code. In fact, inability to obtain the
necessary publications can be an indication that the
code is either not well documented or that the code is
proprietary. In either case, inaccessibility of the
documentation and related publications should be
grounds for evaluating the code as unacceptable.
Most of the items in Table S-3 should be described in
the code documentation, although excessive use of
modeling jargon may make some items difficult to
find. For this reason, some assistance from an
experienced modeler may be required to complete the
evaluation. Conversations with users can also help
decipher cryptic aspects of the documentation.
The evaluation process must rely on user opinions and
published information to take the place of hands-on
experience and testing. User opinions are especially
valuable in determining whether the code functions as
documented or has significant errors (bugs). In some
instances, users have performed extensive testing and
benchmarking or are familiar with published papers
documenting the use of the code. In essence, the
evaluation process substitutes second-hand experience
for first-hand knowledge (user opinions) to shorten the
time it takes to perform the review.
S-15
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Table S-3. Model Selection Criteria
CRITERIA
Section 5.2.1 Administrative Data
Author(s)
Development Objective (research, general use, education)
Organization(s) Distributing the Code
Organization(s) Supporting the Code
Date of First Release
Current Version Number
References (e.g., documentation)
Hardware Requirements
Accessibility of Source Code
Cost
Installed User Base
Computer language (e.g., FORTRAN)
Section 5.2.2
Remedial Process
Scoping
Characterization
Remediation
Section 5.2.3 Site-Related Criteria
Boundary/Source Characteristics
Source Characteristics
Multiple sources
Geometry
line
point
area
Release type
constant
variable
Aquifer System Characteristics
confined aquifers
unconfined aquifers (water-table)
aquitards
multiple aquifers
convertible
Soil/Rock Characteristics
heterogeneity in properties
anisotropy in properties
fractured
macropores
layered soils
Transport and Fate Processes
dispersion
advection
diffusion
density dependent
partitioning between phases
solid-gas
solid-liquid
S-16
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Table S-3. (Continued)
CRITERIA
equilibrium isotherm:
linear (simple retardation)
Langmuir
Freundlich
nonequilibrium isotherm
radioactive decay and chain decay
speciation
Multiphase Fluid Conditions
two-phase water/NAPL
two-phase water/air
three-phase water/NAPL/air
Flow Conditions
fully saturated
variably saturated
Temporal Discretization (steady-state or transient)
Section 5.2.4 Code-Related Criteria
Source Code Availability
History of Use
Code Usability
Quality Assurance
code documentation
code testing
Hardware Requirements
Solution Methodology
Code Output
Code Dimensionality
S-17
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SECTION 1
INTRODUCTION
1.1 BACKGROUND-PURPOSE AND SCOPE OF
THE JOINT EPA/DOE/NRC PROGRAM
The overall joint EPA/DOE/NRC program is
concerned with the selection and use of mathematical
models that simulate the environmental behavior and
impacts of radionuclides via all potential pathways of
exposure, including the air, surface water, ground
water, and terrestrial pathways. Figure 1-1 presents an
overview of the various exposure pathways.
Though the joint program is concerned with all
pathways, it has been determined that, due to the
magnitude of the undertaking, it would be appropriate
to divide the program into smaller, more manageable
phases, corresponding to each of the principal
pathways of exposure. It was also determined that in
the first phase of the project greatest attention would
be given to the ground-water pathways.
Ground-water pathways were selected for
consideration first for several reasons. At a large
number of sites currently regulated by the EPA and the
NRC or owned by the DOE, the principal concern is
the existence of, or potential for, contamination of the
aquifers underlying the various sites. In addition,
relative to the air, surface water, and terrestrial
pathways, ground-water contamination is more
difficult to sample and monitor, thereby necessitating
greater dependence on models to predict the locations
and levels of contamination in the environment.
The types of models used to simulate the behavior of
radionuclides in ground water must be more complex
than surface water and atmospheric pathway transport
models in order to address the more complex settings
and the highly diverse types of settings associated with
different sites. As a result, the methods used to
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1-1
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model ground water have not been standardized to the
same extent as has surface water and air dispersion
modeling, and, therefore, there is considerably less
regulatory guidance regarding appropriate methods for
performing ground-water modeling.
In addition to pathways of exposure, the scope of Phase
1 of the joint program also considered the range of
categories of sites that should be considered. The full
range of sites in the United States that contain
radioactive materials can be divided into the following
categories:
! Federal facilities under the authority of 18 federal
agencies, predominantly consisting of DOE and
Department of Defense (DOD) sites and facilities,
and sites listed on the National Priorities List
(NPL),
! NRC and NRC Agreement State licensed
facilities,
! State licensed facilities,
! Facilities and sites under the authority of the
states but not governed by specific regulations.
These include sites containing elevated levels of
naturally occurring radionuclides (NORM).
All of these sites are of interest to the program.
However, a number of categories of facilities and sites
were excluded from consideration in the joint program
because they are being licensed specifically to receive
radioactive material for storage and disposal; i.e.,
licensed low-level and high-level waste storage and
disposal sites. These sites are being managed within
a highly structured regulatory context to receive
radioactive materials, and, though models are used to
support the siting and design of such facilities, they are
not remedial sites.
It was also necessary to limit the range of the
categories of sites of interest to the program in order to
keep the number of categories of sites to a manageable
size. It was determined that this phase of the project
will be limited to (1) sites currently listed on the NPL
that contain radioactive materials and (2) sites
currently or formerly licensed by the NRC that are part
of the Site Decommissioning Management Program
(SDMP). The SDMP has been established by the
NRC to decommission 46 facilities
that require special attention by the NRC staff.
Ground-water modeling needed to support remedial
decision making at NPL sites containing radioactive
materials is in many ways similar to the ground-water
modeling needs of the SDMP.
These categories of sites were selected for
consideration because decisions are currently being
made regarding their decontamination and
remediation, which, in many cases, require the use of
models to support decision making and demonstrate
compliance with remediation goals. Though the
project is designed to address the modeling needs of
these categories of sites, the information gathered on
this project should have applicability to the full range
of categories of sites concerned with the disposition of
radioactive contamination.
In conclusion, in order to meet its mission of
promoting the appropriate and consistent use of
mathematical models in the remediation and
restorationprocess at sites containing, or contaminated
with, radioactive materials, this first phase of the joint
program is designed to achieve the following four
objectives:
1) Describe the roles of modeling and the
modeling needs at each phase in the remedial
process (MAU93);
2) Identify models in actual use at NPL sites and
facilities licensed under RCRA, at DOE sites,
and at NRC sites undergoing decontamination
and decommissioning (D&D) (PAR92);
3) Produce detailed critical reviews of selected
models in widespread use; and
4) Produce draft guidance for hy drogeologists and
geoscientists tasked with the responsibility of
selecting and reviewing ground-water flow and
transport models used in the remediation,
decommissioning, and restoration process.
This report fulfills the fourth objective of Phase 1 of
the joint program. Specifically, this report describes a
process for reviewing and selecting ground-water flow
and transport models that will aid remedial decision
making during each phase of the remedial process,
from the initial scoping phase, to the detailed
characterization of the site, to the selection and
implementation of remedial alternatives.
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1.2 PURPOSE AND SCOPE OF THIS REPORT
Remedial contractors, with the concurrence of the site
managers, generally select and apply ground-water
flow and transport models. However, unless
specifically trained in ground-water flow and transport
modeling, it is difficult for the site manager to
participate actively in these decisions. Ground-water
flow and transport modeling requires highly
specialized training and experience, and, as a result,
the site manager must usually depend heavily on the
expertise and judgement of staff hydrogeologists as
well as outside contractors and consultants. This
report provides background information that should
help hydrogeologists and geoscientists assist the site
manager in making more informed decisions regarding
the selection and use of ground-water flow and
transport models and computer codes throughout the
remedial process.
Previous reports in this series (MOS92, PAR92) have
determined that the types of models and the processes
that require modeling during the remedial process
depend on a combination of the following five factors:
1. reasons for modeling,
2. contaminant waste characteristics,
3. site environmental characteristics,
4. site land use and demography, and
5. phase of the remedial process.
The principal reasons for modeling that, in part,
influence model selection include: (1) development
and refinement of the site conceptual model from
which hypotheses may be tested, (2) the performance
of risk assessments and the evaluation of compliance
with applicable health and safety regulations, (3) the
design of environmental measurements programs,
primarily to determine the optimal location for
boreholes, and (4) the identification, selection, and
design of remedial alternatives. Each of these reasons
for modeling influences modeling needs and model
selection differently.
A review of the physical, chemical, and radiological
properties of the waste at a number of remedial sites
reveals that the waste characteristics can be diverse.
At sites currently undergoing or scheduled for
remediation, over 30 different types of radionuclides
have been identified, each with its own radiological
and chemical properties. The waste is found in a
variety of chemical forms and physical settings,
including contaminated soil, in ponds, in storage piles
and landfills, buried in trenches, and in tanks and
drums. Each of these physical and chemical settings
influences the areal distribution of the contaminants
and rate at which they may leach into the underlying
aquifer, which, in turn, influences model selection.
In a similar manner, the environmental characteristics
of remedial sites are highly diverse (PAR92). The sites
containing radioactive materials that are currently
undergoing remediation include both humid and dry
sites, sites with and without an extensive unsaturated
zone, and sites with simple and complex
hydrogeological characteristics. These different
environmental settings determine the processes that
need to be modeled, which, in turn, influence the
selection of models and computer codes.
The land use and demographic patterns at a site,
especially the location and extent of ground-water use,
affect the types and complexity of the models required
to assess the potential impacts of the site on public
health. At many of the sites contaminated with
radioactive materials, the principal concern is the use
of the ground water by current or future residents
located close to, and downgradient from, the source of
contamination. At other sites, the concern is the use of
private and municipal wells located at some distance
and in a variety of directions from the source. Each of
these usage patterns influences the selection of ground-
water flow and transport models and computer codes.
Superimposed on these waste and site-related issues
are the different modeling needs associated with the
various phases of the remedial process. The phase of
the remedial process from scoping and planning, to
site characterization, to remediation, creates widely
different opportunities for modeling, which, together
with the other factors, influences model and code
selection.
This report describes the methods for selecting ground-
water flow and transport models and computer codes
that meet the modeling needs at sites contaminated
with radioactive materials. The selection process is
described in terms of the various site characteristics
and processes requiring modeling and the availability,
reliability, and costs of the computer codes that meet
the modeling needs.
Though this report is limited to a discussion of the
model selection process, it is recognized that the
proper application of the selected models is as
important, if not more important, than model selection.
A model, no matter how well suited to a particular
application, could give erroneous and highly
1-3
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misleading results if used improperly or with
incomplete or erroneous input data. Conversely, even
a model with very limited capabilities, or a model used
at a site which has not been well characterized, can
give very useful results if used intelligently and with a
full appreciation of the limitations of the model and
the input data. It is not possible within the scope of
this project to address model applications, quality
control, and the presentation and interpretation of
modeling results. Future reports prepared under this
program will address these important topics.
1.3 PRINCIPAL SOURCES OF INFORMATION
In accomplishing its objectives, this report makes use
of the information contained in the previous reports
prepared on this program, including:
! "Environmental Pathway Models - Ground Water
Modeling in Support of Remedial Decision
Making at Sites Contaminated with Radioactive
Material," EPA 402-R-93-009, March 1993.
! "Environmental Characteristics of EPA, NRC,
and DOE Sites Contaminated with Radioactive
Substances," EPA 402-R-93-001, March 1993.
! "Computer Models Used to Support Cleanup
Decision Making at Hazardous and Radioactive
Waste Sites," EPA 402-R-93-005, March 1993.
In addition, extensive use was made of:
! "Superfund Exposure Assessment Manual,"
EPA/540/1-88/001, April 1988.
! "Leachate Plume Management," EPA/540/2-
85/004, November 1985.
! IMES, "Integrated Model Evaluation System,"
Prototype, Version 1, September 1991.
Developed by Versar, Inc. for the Exposure
Assessment Group, Office of Health and
Environmental Assessment, Office of Research
and Development, Environmental Protection
Agency.
Finally, this report relies heavily on the experience
gained by the project team during the review of three
existing codes: RESRAD, VAM2D, and MT3D. As
part of this project, these three computer codes were
reviewed as if they were being considered for use on a
remedial project. The review of these codes, including
the process used to review these codes, has been
documented in a separate report (EPA 402-R-93-005)
in this series. The procedures used to perform these
reviews contributed to the generic guidance presented
in this report.
1.4 KEY TERMS
A glossary of terms used in this report is presented in
Appendix A. In addition, an index directs the reader
to the pages in the report where key terms are defined
and discussed. Described below are three key
terms/concepts that are fundamental to understanding
the report.
Conceptual Model. The conceptual model of a site is
a flow diagram, sketch, and/or description of a site and
its setting. The conceptual model describes the
subsurface physical system including the nature,
properties, and variability of the aquifer system (e.g.,
aquifers, confining units), and also depicts the types of
contaminants/wastes at a site, where they are located,
and how they are being transported offsite by runoff,
percolation into the ground and transport offsite in
ground water, or suspension or volatization into the air
and transport by the prevailing meteorological
conditions. The conceptual model also attempts to
help visualize the direction and path followed by the
contaminants, the actual or potential locations of the
receptors, and the ways in which receptors may be
exposed, such as direct contact with the source,
ingestion of contaminated food or water, or inhalation
of airborne contaminants. As information regarding a
site accumulates, the conceptual model is continually
revised and refined.
Mathematical Model. A mathematical model
translates the conceptual model into a series of
equations which, at a minimum, describe the geometry
and dimensionality of the system, initial and boundary
conditions, time dependence, and the nature of the
relevant physical and chemical processes. The
mathematical model essentially transforms the
conceptual model to the level of mathematical accuracy
needed to support remedial decision making.
Computer Code. A computer code is simply a tool that
is used to solve the equations which constitute the
mathematical model of the site and display the results
in a manner convenient to support remedial decision
making.
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1.5 ORGANIZATION OF THE REPORT
This report is divided into five sections. Following
this introduction, Section 2 presents an overview of the
types of ground-water modeling decisions facing the
site remediation manager. The section is designed to
help the site manager determine the role of, and need
for, modeling in support of remedial decision making.
Section 3 addresses the construction of a conceptual
model of a site and how it is used in the initial
planning and scoping phases of a site remediation,
especially as it pertains to the selection and use of
ground-water flow and contaminant transport models.
Section 4 describes the various site characteristics and
ground-water flow and contaminant transport
processes that may need to be explicitly modeled. The
purpose of this section is to help the site manager
recognize the conditions under which specific model
features and capabilities are needed to support
remedial decision making during each phase in the site
remediation process.
Section 5 summarizes the computer code attributes that
should be considered for screening and selecting the
potential computer codes that are best suited to meet
site-specific modeling needs.
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SECTION 2
MODELING DECISIONS FACING THE SITE
REMEDIATION MANAGER
A review of current regulations and guidelines pertaining to the remediation of sites on the National Priorities List and
in the Nuclear Regulatory Commission's Sites Decommissioning Management Program (SDMP) reveals that fate and
effects modeling is not explicitly required. However, in order to make informed and defensible remedial decisions,
ground-water flow and transport modeling can be useful. This section presents a methodology for determining when
ground water may be a significant pathway of exposure and discusses the roles ground-water modeling may play in
support of remedial decision making. The section concludes with a discussion of the various resources available to the
remediation manager to help in identifying and fulfilling modeling needs.
2.1 IS GROUND WATER A POTENTIALLY
IMPORTANT EXPOSURE PATHWAY?
The ground-water pathway may be considered a
potentially significant exposure pathway if: (1) the
radionuclide concentrations in the ground water
exceed the levels acceptable to the cognizant regulatory
authorities; or (2) the contamination at the site could
eventually cause the radionuclide concentrations in
ground water to exceed the applicable criteria. On this
basis, if the measured concentrations of radionuclides
in ground water downgradient from the site, or in
leachate at the site, exceed the applicable criteria, and
the ground water in the vicinity of the site is being
used, or has the potential to be used as a source of
drinking water, it is likely that ground-water modeling
will be useful, if not necessary, in support of remedial
decision making at the site.
Until additional regulatory guidance is available, the
drinking water standards set forth in 40 CFR 141
should guide remedial decision making. Section 1412
of the Safe Drinking Water Act (SDWA), as amended
in 1986, requires EPA to publish Maximum
Contaminant Level Goals (MCLGs) and promulgate
National Primary Drinking Water Regulations for
contaminants in drinking water which may cause any
adverse effects on the health of persons and which are
known or anticipated to occur in public water systems.
On July 9, 1976, the EPA published "Interim Primary
Drinking Water Regulations, Promulgation of
Regulations on Radionuclides" (41 FR 28402).
The interim rule establishes maximum contaminant
levels (MCL) for radionuclides in community water.
The MCLs limit the concentration of radionuclides at
the tap to:
! 5 pCi/L for Ra-226 plus Ra-228.
! 15 pCi/L for gro ss alpha, including Ra-226 but
excluding radon and uranium.
! that concentration of manmade beta/gamma
emitting radionuclides that could cause
4 mrem/yr to the whole body or any organ.
The regulation applies to community public water
systems regularly serving at least 25 persons
year-round or having at least 15 connections used
year-round.
In response to a need to finalize the rule, expand the
regulations to include uranium and radon, and revise
and refine the rule, the EPA published an Advanced
Notice of Proposed Rulemaking (ANPR) on September
30,1986(51FR 34836), and onJuly 18,1991theEPA
issued an NPR entitled "National Primary Drinking
Water Regulations; Radionuclides" (56 FR 33050). 40
CFR 191 is being finalized.
As in the interim rule, the proposed rule applies to all
community, and all non-transient, non-community
public water systems regularly serving at least 25
persons year-round or having at least 15 connections
used year-round. The proposed standards establish the
following requirements:
The Maximum Contaminant Level Goal (MCLG)
for all radionuclides is zero since radionuclides are
known carcinogens. MCLGs are non-enforceable
health goals that are set at levels at which no known
or anticipated adverse effects on the health of
persons occur and which allow an adequate margin
of safety.
The MCLs are as follows:
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Radionuclide
MCL
Ra-226 20 pCi/L
Ra-228 20 pCi/L
Rn-222 300 pCi/L
Uranium 20 ug/L (30 pCi/L)
Beta and photon emitters
(excluding Ra-228) 4 mrem/yr EDE
Adjusted gross alpha
emitters (excluding
Ra-226, U, and Rn 222) 15 pCi/L
MCLs are enforceable standards set as close to the
MCLGs as is feasible, including economic factors.
The proposed rule also establishes specific
requirements regarding the use of control and
treatment technologies and monitoring and reporting
requirements.
The drinking water standards are fundamental health-
based standards that apply to public sources of
drinking water. In addition, the drinking water
standards have also had extensive use as applicable or
relevant and appropriate regulations (ARARs) forNPL
sites. As an ARAR, if the observed concentrations of
radionuclides in drinking water supplies coveredby the
rule exceed the MCLs, the rule applies directly and
remedial actions are required. If the potential exists
for ground-water contamination to exceed the MCLs,
the rule is considered relevant and appropriate.
For NPL sites, the Hazard Ranking System (HRS)
scoring package provides information that will help in
determining if ground-water modeling is needed at a
site. Specifically, Section 7.1.1 of the HRS requires
the sampling and analysis of ground water to
determine if ground-water contamination is present.
If radionuclide concentrations in ground water in
excess of background are found and exceed the Level
I benchmarks delineated in Sections 2.5.2 and 7.3.2 of
the HRS (these benchmarks are keyed to the MCLs),
ground-water contamination is a concern at the site,
and ground-water modeling will likely be needed to
support the baseline risk assessment and remedial
decision making.
At some sites, information may not be available
regarding the levels of radionuclide contamination in
ground water or leachate. Alternatively, radionuclide
measurements may have been made, but yield
inconclusive results. Under these conditions, an
estimate needs to be made of the radionuclide
concentrations in the soil or the waste at the site,
which can then be used to determine if the potential
exists for exceeding the applicable criteria.
For NPL sites, the information needed to make this
determination is likely to be available in the HRS
scoring package addressing Hazardous Waste Quantity
and Likelihood of Release. The preferred method for
scoring Hazardous Waste Quantity (Section 7.2.5.1 of
the HRS) requires information on the concentration of
individual radionuclides at the site and the volume and
area of the contamination.
Given the radionuclide concentrations in soil or waste,
the radionuclide concentration in leachate can be
estimated using partition factors. A partition factor
establishes the equilibrium relationship between the
average radionuclide concentration in soil or waste and
that in leachate. If the product of the radionuclide
concentrations with the appropriate partition factors
results in radionuclide concentrations in leachate
significantly in excess of the applicable criteria, it may
be concluded that the radionuclide concentrations in
ground water in the vicinity of the site could exceed
the criteria, thereby requiring ground-water modeling
to assess the potential impacts on nearby user
locations.
Once the leachate comes into contact with the
underlying soil, a new equilibrium begins to be
established between the leachate and the soil. The
equilibrium ratio of the radionuclide concentration in
the soil to that in the water in intimate contact with the
soil is referred to as the distribution coefficient (Kd).
Once site-specific Kds are determined or appropriate
generic Kds are identified, the radionuclide
concentration in the soil divided by the Kd for each
radionuclide yields a crude estimate of the
concentration of the radionuclide in the soil pore water
percolating through the soil.
Though partition factors are highly site specific,
generic values have been used in the past for screening
calculations which are designed to provide reasonable
upper bound radionuclide concentrations in leachate
and ground water. Examples of generic partition
factors are provided in NRC86. Tabulations of Kd
values that have had widespread application are
provided in BAE83 and SHE90.
If either the measured or derived values for the
radionuclide concentrations in ground water exceed
the applicable criteria, resources need to be put into
place to perform ground-water modeling.
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2.2 REASONS FOR MODELING
Once it is determined that the ground-water exposure
pathway is potentially important, ground-water flow
and transport modeling can have a wide range of uses
in support of remedial decision making. Table 2-1
presents the principal reasons for modeling on a
remedial project. These uses can surface during any
phase of the remedial process. However, some of these
reasons are more likely to occur during specific phases
of a remedial project.
In Table 2-1, scoping and planning occur early in the
project, wherein regional, sub-regional, and site-
specific data are reviewed and analyzed in order to
define the additional data and analyses needed to
support remedial decision making. In the site
characterization phase, the plans developed during the
scoping phase are implemented. These data are used
to characterize more fully the nature and extent of the
contamination at the site, to define the environmental
and demographic characteristics of the site, and to
support assessments of the actual or potential impacts
of the site. The results of the site characterization
phase are analyzed to determine compliance with
applicable regulations and to begin to define strategies
for the remediation of the site. In the site remediation
phase, alternative remedies are identified, evaluated,
selected, and implemented.
During scoping and planning, modeling can be used to
identify the potentially significant radionuclides and
pathways of exposure, which, in turn, can be used to
support the design of comprehensive and cost-effective
waste characterization, environmental measurements,
and site characterization programs. During site
characterization, modeling is used primarily in support
of dose and risk assessment of the site and to evaluate
the adequacy of the site characterization program.
During the remediation phase, modeling is used
primarily to support the selection and implementation
of alternative remedies and, along with environmental
measurements programs, is used to determine the
degree to which the remedy has achieved the remedial
goals.
Table 2-1 attempts to identify those opportunities for
modeling that are more likely to surface during the
different phases of the remedial process. In general,
the remedial phase often dictates the types of remedial
decisions that need to be made and the amount of site-
specific information and time available to make these
decisions. These, in turn, determine the role of
modeling. For example, during scoping, it may not be
feasible to gain access to sampling locations, and the
only way to predict the potential impacts of a source of
contaminants is by modeling. During site
characterization, sampling locations are generally
accessible; however, the contaminant may have notyet
reached a receptor location. Accordingly, modeling is
used to predict future impacts. During remedy
selection, modeling is used to simulate the
performance of a remedy in order to evaluate its cost-
effectiveness and refine its design.
2.3 PLANNING FOR MODELING
2.3.1 Identifying Modeling Needs
Given the phase in the remedial process and the
reasons for modeling, the types of models and the
input data required to run the models are determined
by the characteristics of the waste, the site
hydrogeological setting and characteristics, and the
current and projected ground-water use in the vicinity
of the site. Accordingly, the role of and need for
modeling, and the types of models and associated input
data, are determined by a combination of five factors:
! phase of the remedial process,
! reasons for modeling,
! waste characteristics,
! hydrogeological characteristics, and
! local land use and demography.
In order to make informed decisions regarding the
selection and application of ground-water flow and
transport models and the interpretation of the results,
the remediation manager will require site-specific
information on each of these five factors. The first two
factors are related and are largely determined by the
regulatory structure within which remedial decisions
are being made. The last three factors are of a more
technical nature and usually require highly specialized
expertise to relate the waste, hydrogeologic, and
demographic characteristics of a site to the models
suited to these characteristics and the reasons for
modeling.
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Table 2-1. Matrix of Reasons for Modeling
Opportunities for Modeling
1.
2.
3.
4.
5.
6.
7.
8.
When it is not feasible to perform field
measurements, i.e.,
! Cannot get access to sampling locations
! Budget is limited
! Time is limited
When there is concern that downgradient locations
may become contaminated at some time in the future.
When field data alone are not sufficient to
characterize fully the nature and extent of the
contamination; i.e.,
! when field sampling is limited in space and time
and needs to be supplemented with models
! when field sampling results are ambiguous or
suspect
When there is concern that conditions at a site may
change, thereby changing the fate and transport of
the contaminants; i.e.,
! seasonal changes in environmental conditions
! severe weather (floods, tornadoes)
! accidents (fire)
When there is concern that institutional control at the
site may be lost at some time in the future resulting
in unusual exposure scenarios or a change in the fate
and transport of the contaminants; i.e.,
! trespassers
! inadvertent intruder
! (construction/agriculture)
! drilling, mineral exploration, mining
! human intervention (drilling, excavations,
mining)
When remedial actions are planned and there is a
need to predict the effectiveness of alternative
remedies.
When there is a need to predict the time when the
concentration of specific contaminants at specific
locations will decline to acceptable levels (e.g.,
natural flushing).
When there is concern that at some time in the past
individuals were exposed to elevated levels of
contamination and it is desirable to reconstruct the
doses.
Scoping1
M
M
M
F
F
F
F
F
Site
Characterization1
F
M
M
M
M
F
M
M
Remediation1
F
M
M
M
M
M
M
F
1. M Denotes an important role.
F Denotes a less important role.
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Table 2-1. (Continued)
Opportunities for Modeling
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
When there is concern that contaminants may be
present but below the lower limits of detection.
When field measurements reveal the presence of
some contaminants and it is desirable to determine if
and when other contaminants associated with the
source may arrive, and at what levels.
When field measurements reveal the presence of
contaminants and it is desirable to identify the source
or sources of the contamination.
When there is a need to determine the timing of the
remedy; i.e., if the remedy is delayed, is there a
potential for environmental or public health impacts
in the future?
When there is a need to determine remedial action
priorities.
When demonstrating compliance with regulatory
requirements.
When estimating the benefit in a cost-benefit analysis
of alternative remedies.
When performing a quantitative dose or risk
assessment.
When designing the site characterization program
and identifying exposure pathways of potential
significance.
When there is a need to compute or predict the
concentration distribution in space and time of
daughter products from the original source of
radionuclides.
When there is a need to quantify the degree of
uncertainty in the anticipated behavior of the
radionuclides in the environment and the associated
doses and risks.
When communicating with the public about the
potential impacts of the site and the benefits of the
selected remedy.
Scoping1
F
F
M
F
F
M
F
F
M
M
M
M
Site
Characterization1
M
M
M
F
F
M
F
M
F
F
F
F
Remediation1
F
F
F
M
M
M
M
M
M
F
F
M
Source: EPA93
1. M Denotes an important role.
F Denotes a less important role.
2-5
-------
Recognizing the need for modeling, and identifying
and applying the models that meet these needs, unfolds
as the project matures. Modeling decisions are based
on site-specific information pertaining to each of the
above five factors and the combined judgement of
regulatory and technical specialists. Modeling
decisions cannot be made in a "cookbook" fashion.
Accordingly, during the initial phases of a remedial
project and throughout the remedial process, the
remediation manager must continually assess the need
to employ models. Table 2-1 can be useful in
determining when these needs exist or may arise.
Once the modeling needs are recognized, it is
appropriate to determine or define the form of the
results or output of the modeling exercise. The
following presents the various types of output resulting
from a given modeling exercise for sites containing
radioactive material.
! The time-averaged and time-varying radionuclide
concentrations in air, surface water, ground water,
soil, and food items. These are usually expressed in
units of pCi/L of water or pCi/kg of soil or food
item. The time-averaged values are used to
determine the annual radiation doses and risks
and/or compliance with ARARs that are expressed
as average, as opposed to peak values. The time-
varying values are useful in determining arrival
times of contaminants at receptor locations, which
can help in prioritizing sites, or the impacts of
accidental releases, which are often one-time, short-
term occurrences.
! The radiation field in the vicinity of radioactive
material, expressed in units of uR/hr. Estimates of
exposure rate, whether measured or predicted, are
useful in protecting members of the public or
workers who may be present in, or need to enter, the
radiation field.
! The transit time or time of arrival of a radionuclide
at a receptor location. This measure is useful in
determining at what point in the future a source of
contamination has the potential to adversely affect
receptors.
! The volume of water contained within or moving
through a hydrogeological setting.
! Potentiometric surfaces (i.e., heads) are commonly
output from ground-water flow models from which
ground water/contaminant flow paths and/or capture
zones can be determined.
! Radiation doses to individual members of the public
under quasi-steady state and changing conditions
and following accidents. The doses are evaluated
for the site in its current condition (i.e., the no
action alternative) and during and following a broad
range of feasible alternative remedies. These are
usually expressed in units of mrem/yr effective dose
equivalent (EDE) for continuous exposures and
mrem per event (EDE) for transients and postulated
accidents. Most radiation protection standards are
expressed in units of the dose to individuals.
! Radiation risks to individual members of the public
under expected and transient conditions and
following accidents. The risks are evaluated for the
no action alternative and during and following a
broad range of feasible remedies. These are usually
expressed in units of individual lifetime risk of total
and fatal cancers. In addition to individual dose,
individual risk is used to characterize the impacts on
public health and is required by the National
Contingency Plan (NCP).
! Cumulative radiation doses to the population in the
vicinity of the site under expected and transient
conditions and following accidents. The cumulative
doses are evaluated for the no action alternative and
during and following a broad range of feasible
remedies. These are usually expressed in units of
person rem/yr (EDE) for continuous exposures and
person rem per event (EDE) for transients and
accidents.
! Cumulative radiation risks to the population in the
vicinity of the site under expected and transient
conditions and following accidents. The cumulative
population risks are evaluated for the no action
alternative and during and following a broad range
of feasible remedies. These are usually expressed
in units of total and fatal cancers per year for
continuous exposures or per event for transients and
accidents in the exposed population.
! Radiation doses and risks to remedial workers for a
broad range of alternative remedies. The units of
dose and risk for individual and cumulative
exposures are the same as those for members of the
public.
! Uncertainties in the above impacts, expressed as a
range of values or a cumulative probability
2-6
-------
distribution of dose and risk.
The specific regulatory requirements that apply to the
remedial program determine which of these "end
products" is needed. In general, these modeling results
are used to assess impacts or compliance with
applicable regulations; however, information regarding
flux, transport times, and plume arrival times is also
used to support a broad range of remedial decisions.
These modeling endpoints must be clearly defined,
since the type of endpoint will help to determine the
type of ground-water flow and transport model that
will support the endpoint of interest. For example, a
baseline risk assessment at a site contaminated with
radioactive material is used in determining the annual
radiation dose to an individual drinking water obtained
from a potentially contaminated well. The endpoint in
this case is the dose to an individual expressed in units
of mrem/yr. In order to estimate this dose, it is
necessary to estimate the average concentration of
radionuclides in the well water over the course of a
year. The models, input parameters, and assumptions
needed to predict the annual average radionuclide
concentration are different than those needed to predict
the time-varying concentration at a given location.
The latter usually requires much more input data and
models capable of simulating dynamic processes.
2.3.2 Sources of Assistance
Once the remediation manager has identified the role
modeling will play on the remedial project (see Table
2-1) and the forms of the results of the modeling
exercise, resources must be put into place to meet these
needs. These resources include access to technical
expertise and a broad range of ground-water flow and
transport models.
In response to the need for ground-water flow and
transport modeling in support of remedial decision
making, guidance and assistance are becoming
increasingly available. Appendix B briefly
summarizes some of the resources available to a
remediation manager, organized according to the
following categories:
! Branches and Divisions within Agencies
! Expert Systems
! Electronic Bulletin Boards
! Electronic Networks
2.3.2.1 Branches and Divisions Within Agencies
Environmental Protection Agency
Technical assistance available to EPA remediation
managers is described in "Technical Assistance
Directory," CERI-91-29, July 1991.
Nuclear Regulatory Commission
Technical assistance to NRC personnel with regulatory
oversight responsibility for the decontamination and
decommissioning of licensed facilities is available
from the Office of Nuclear Material Safety and
Safeguards (NMSS).
Department of Energy
Technical guidance for DOE and DOE contractor
personnel with responsibility for environmental
restoration and waste management at DOE facilities is
provided through the Office of Environmental, Safety,
and Health. In addition, since many of the DOE sites
are on the NPL, EPA technical assistance can also be
accessed.
2.3.2.2 Electronic Media
Electronic communication media are becoming a
common means by which individuals participate in
forums where expertise is freely shared. Institutions
whose mandate includes the dissemination of expert
advice and information also use these media. These
forms of communication result from the direct
transmittal of computer media (e.g., tape, diskette, CD-
ROM, etc.) or utilize remotely accessed computer
systems consisting of dedicated hardware and
associated software. In remote systems, the user can
access the system via modem or some other hard-wired
connection and retrieve from or transmit to the system
information as required.
Electronic media offer great potential to assist ground-
water model users and reviewers. It is possible to
classify these media into three types, namely bulletin
boards (restricted access), networks (general access),
and expert systems. Although the first two systems
operate similarly and share some approaches to
providing their services, they differ in the way that
they are used. A brief overview of these instruments
follows. Specific examples of these resources are
presented in Appendix B.
2-7
-------
Bulletin Boards
Bulletin boards exist at a specific location maintained
by an identifiable individual or institution. Bulletin
boards usually contain facilities for posting electronic
mail and allow the user to participate in one or more
conferences - more-or-less structured discussions on
specific topics. In addition, most bulletin boards
contain archives of files consisting of various data
bases, executable programs, and notices.
Networks
A computer network consists of a number (in some
cases many thousands) of individual computers (nodes)
tied together by hardware and some network software
that regulates access to the system and the transfer of
information between nodes. Most network discussion
groups are moderated by an individual or group of
individuals. Networks can be and are used to post
electronic mail in much the same way as one would
post mail on a bulletin board. However, they have the
additional capability of "broadcasting" information to
a much more general audience. Networks are a good
way to get answers to problems when the user is
unsure of who might possibly provide those answers.
An even more powerful aspect of some networks is the
ability to run software on one of the network nodes
in real-time from a
remote location with immediate feedback. Most
bulletin boards don't allow that level of access.
Expert Systems
Expert systems are software packages which guide a
user through the solution of a problem by asking a
series of questions and/or by providing a series of pre-
programmed answers to those questions. An example
of such a system that can be used in the selection of an
appropriate code for air, surface, or ground-water
modeling is the Integrated Model Evaluation System
available from the Environmental Protection Agency.
Both bulletin boards and networks are effective in
obtaining non-urgent help on focused issues and for
keeping up with fast-changing subjects - they are not
particularly useful if the user needs information
quickly or cannot phrase a question succinctly and
clearly. Many bulletin boards and networks are free to
the user while others are based on some fee system.
Nearly all remotely accessed electronic media require
some form of registration before use, either by written
request and registration or by on-line registration
during the user's first session. Expert systems will
usually offer the fastest and most in-depth answers to
specific problems. But expert systems can be quickly
outdated if the data (knowledge) base on which they
depend changes. The "learning curve" for all three
types of electronic information exchange is fairly quick
- a user can request and/or obtain useful information in
a matter of minutes to hours.
-------
SECTION 3
CONSTRUCTING AND REFINING THE CONCEPTUAL MODEL
OF THE SITE
For sites on the NPL, the development of a conceptual model of the site is identified as a specific step in the scoping
stage of the RI/RS process (see EPA88). However, the need for conceptual modeling applies to any site undergoing
remediation. Figure 3-1, taken from EPA88, is an example of a conceptual model. It identifies the various pathways
that may contribute to the potential current and future impacts of the site on public health and the environment.
Accordingly, the construction of a conceptual model of a site is the first step in determining modeling needs and
identifying models that meet these needs. This section presents a brief discussion of basic concepts pertinent to the
construction of a conceptual model of the site with respect to the ground-water pathway for sites contaminated with
radionuclides.
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3.1 BASIC QUESTIONS THAT WILL NEED TO
BE ANSWERED
For sites where ground-water contamination is
identified as a potentially important exposure pathway,
the planning effort should attempt to answer the
following typical questions:
! Do the radionuclides have relatively long or short
half-lives and do they have radioactive daughters?
! Do the contaminants enter the ground-water flow
system at a point, or are they distributed along a
line or over an area (or volume)?
! Does the source consist of an initial pulse of
contaminant or is it constant over time?
! Is there a thick unsaturated zone?
! Is the lithography relatively homogeneous or does
it contain multiple layers?
! How will the hydrogeology affect flow and
transport?
! At what rate will the radionuclides be transported
relative to ground-water flow?
! Are there nearby wells or other hydraulic
boundaries that could influence ground-water
flow?
! What is the nature of the system boundaries?
! Where are the current or future receptors located?
Can they influence ground-water flow?
The answers to these questions will help to identify the
types of processes that may need to be modeled at the
site, which, in turn, will help in screening the types of
models and computer codes appropriate for the site. A
discussion of the various flow and transport processes
and the site characteristics that influence these
processes is provided in EPA88.
During the scoping phase, it will not be possible, nor
necessary, to answer these questions with certainty.
However, as site characterization proceeds,
information will become available that will help to
develop more complete answers to these questions. In
fact, a well-designed site characterization program will
obtain data that will help answer these questions.
3.2 COMPONENTS OF THE CONCEPTUAL
MODEL FOR THE GROUND-WATER
PATHWAYS
The components that make up the initial conceptual
model of the site include:
1. the contaminant/waste characteristics,
2. the site characteristics, and
3. land use and demography.
As the remedial process progresses from initial scoping
and planning to detailed characterization to
remediation, the site characterization becomes more
precise and complete. The following sections discuss
each of these components of a conceptual model and
how they can influence model selection.
3.2.1 Contaminant/Waste Characteristics
To the extent feasible, the site conceptual model should
address the following characteristics of the waste:
! Types of radionuclides
! Waste form and containment
! Source geometry (e.g., volume, area, depth,
homogeneity)
! Physical and chemical properties of the
radionuclides
! Geochemical setting
Within the context of ground-water modeling, these
characteristics are pertinent to modeling the source
term, i.e., the rate at which radionuclides are
mobilized from the waste and enter the unsaturated
and saturated zones.
Types of Radionuclides
One of the most important characteristics in
developing a conceptual model of the site is identifying
the type and approximate quantities of the
radionuclides present. This will not only determine
the potential offsite impacts of the site, it will also help
3-2
-------
to identify the potential magnitude of the risks to
workers, the mobility of the radionuclides, and the
time period over which the radionuclides may be
hazardous. The types of radionuclides will also
determine whether radioactive decay and the ingrowth
of daughters are important parameters that will need to
be modeled.
Waste Form and Containment
Radioactive contaminants are present in a wide variety
of waste forms that influence their mobility. However,
in most cases, the radionuclides of concern are long-
lived, and the integrity of the waste form or container
cannot be relied upon for long periods of time.
Therefore, the source term is often conservatively
modeled as a uniform point, areal, or volume source,
and no credit is taken for waste form or
containerization (EPA92).
If it is desired to model explicitly the performance of
the waste form (e.g., rate of degradation of solidified
waste or containerized waste) or transport in a
complex geochemical environment (changing acidity,
presence of chelating agents or organics), complex
geochemical models may be needed. Depending on
the waste form and container, such models would need
to simulate the degradation rate of concrete, the
corrosion rate of steel, and the leaching rate of
radionuclides associated with various waste forms (i.e.,
soil, plastic, paper, wood, spent resin, concrete, glass,
etc.). These processes depend, in part, on the local
geochemical setting. However, it is generally
acknowledged that it is not within the current state-of-
the-art to explicitly model the geochemical processes
responsible for the degradation of the waste containers
or the waste itself (NRC 90).
Physical and Chemical Properties of the
Radionuclides
If feasible, the conceptual model of the site should
describe the radionuclides and their physical and
chemical characteristics. These parameters may be
pertinent to model selection because certain
radionuclides have properties that are difficult to
model. For instance, most of the NPL and SDMP sites
are contaminated with thorium and uranium, both of
which decay into multiple daughters which may differ
from their parents both physically and chemically.
Some of the radionuclides (e.g., uranium) exhibit
complex geochemistry and their mobility is dependent
upon the redox conditions at the site. Though the
chemical form of the radionuclides and the
geochemical setting can have a profound effect on the
transport of the radionuclides, it is generally
acknowledged reliable modeling of the various
geochemical processes is not often feasible.
Accordingly, during the construction of a site
conceptual model, detailed information regarding the
chemical composition of the radionuclides may not be
necessary. The degree to which this type of
information will be needed to support remedial
decision making will surface as site characterization
proceeds.
Geochemical Setting
In addition to the standard chemical properties of
radionuclides, it is important to understand the
geochemical properties and processes that may affect
transport of the radionuclides that are specific to the
site. These properties and processes include the
following:
! Complexation of radionuclides with other
constituents
! Phase transformations of the radionuclides
! Adsorption and desorption
! Radionuclide solubilities at ambient geochemical
conditions
If it is desired to model these processes explicitly, as
opposed to using simplifying assumptions, such as
default or aggregate retardation coefficients, more
complex geochemical models may be needed.
However, as discussed above, it is currently not often
feasible to explicitly model complex geochemical
processes.
3.2.2 Environmental Characteristics
The conceptual model of the site should begin to
address the complexity of the environmental and
hydrogeological setting. A complex setting, such as a
complex lithology, a thick unsaturated zone, and/or
streams or other bodies of water on site (i.e., a complex
site), generally indicates that the direction and velocity
of ground-water flow and radionuclide transport at the
site cannot be reliably simulated using simple one-
dimensional, analytical models (see Appendix C).
3-3
-------
At more complex sites, such as many of the defense
facilities on the NPL, the remedial process is gener-
ally structured so that, as the investigation proceeds,
additional data become available to support ground-
water modeling. An understanding of the physical
system, at least at a sub-regional scale, may allow an
early determination of the types of models appropriate
for use at the site. Specifically, during the early phases
of the remedial process, when site-specific data are
limited, the following site characteristics may be
extrapolated from regional-scale information and will,
in part, determine the types and complexity of models
required:
! Approximate depth to ground water
! Ground-water flow patterns
! Lithology of the underlying rocks (e.g., limestone,
basalt, shale)
! Presence of surface water bodies
! Land surface topography
! Sub-regional recharge and discharge areas
! Processes or conditions that vary
significantly in time
Even at complex sites, complex computer models may
not be needed. For example, if a conservative
approach is taken, where transport through the
unsaturated zone is assumed to be instantaneous, then
the complex processes associated with flow and
transport through the unsaturated zone would not need
to be modeled. Such an approach would be
appropriate at sites that are relatively small and where
the extent of the contamination is well defined. Under
these conditions, the remedy is likely to be removal of
the contaminated surface and near-surface material.
Examples of these conditions are many of the SDMP
sites and several of the non-defense NPL sites. In
these cases, the use of conservative screening models,
along with site data, may be sufficient to support
remedial decision making throughout the remedial
process.
Depth to Ground Water
Sites located in the arid west and southwest (e.g.,
Pantex, Hanford, and INEL) generally have greater
depths to ground water. The simulation of flow and
transport through the unsaturated zone will generally
require more complex computer codes due to the non-
linearity of the governing equations. Modeling of the
unsaturated zone is further hampered because the
necessary data are often difficult to obtain.
Ground-Water Flow Patterns
The intricacy of the ground-water flow patterns will
have a significant impact on the complexity of the
required modeling. The dominating factors that
control the flow patterns are both the geology and
hydraulic boundaries. Flow in the saturated zone will
tend to be uniform and steady in hydrogeologic
systems that have uncomplicated geology and
boundary conditions that are relatively stable with
time. Uniform flow refers to flow that is in one
direction and does not vary across the width of the flow
field. Steady flow does not change over time.
Boundary conditions, such as constant
pumping/injection and recharge from perennial lakes
and streams, are generally constant over time.
Hy drogeological features that indicate that flow may be
unsteady and nonuniform are areas where discrete
geologic features are known to exist (e.g., faults,
fractures, solution channels), as well as hydraulic
boundaries which may consist of ephemeral streams,
highly variable rainfall, and areas occasionally
indurated by flooding.
Sub-Regional Lithology
The lithology of the underlying rocks also provides
insight into the expected level of difficulty of
modeling. A number of the NPL sites overlie areas
where fractures are probably dominant mechanisms for
flow and transport. These sites include Hanford, Idaho
National Engineering Laboratory (INEL), Maxey Flats,
Jacksonville, Oak Ridge, West Valley, and Pensacola
Air Stations. In some cases, such as at Hanford, the
fractured zone is deep below the site, and concerns
regarding ground-water contamination are limited
primarily to the near-surface sedimentary rock.
It is unlikely that analytical models could be used to
adequately describe flow and transport in the fractured
systems because radionuclide transport and ground-
water flow in fractured media are much more complex
than in unfractured granular porous media. For that
3-4
-------
matter, it generally requires very specialized numerical
codes to simulate flow and transport in fractured
media. This is because of the extreme heterogeneity
and anisotropy associated with the fractures.
Surface Water Bodies
Virtually all of the NPL sites and many of the SDMP
sites have surface water bodies at or in the immediate
vicinity of the site. Bodies of water often have a
significant impact on the ground-water flow and can
seldom be neglected in the modeling analysis. In
general, analytical models are limited in their ability to
simulate properly the effect that surface water bodies
have on contaminant flow and transport, particularly
if the surface water body behaves episo-dically, such as
tidal or wetland areas. Several of the NPL sites are
inundated with wetlands, including Oak Ridge, Himco,
and Shpack Landfill. At least two sites, Pensacola and
Jacksonville, are close to estuaries, which suggests that
tidal as well as density-dependent flow and transport
may be significant.
Sub-Regional Topography
The land surface topography is often overlooked in
developing a site conceptual model but may be an
important factor in evaluating the need for, and
complexity of, ground-water modeling. Topography
may significantly influence ground-water flow
patterns. For instance, Maxey Flats is situated atop a
relatively steep-sided plateau with a stream located at
the bottom of the slope. The steep topo-graphy
strongly controls the direction of ground-water flow,
making it much more predictable. Furthermore,
estimating the flux of ground water moving into the
system from upgradient sources becomes much simpler
if the area of interest is a local recharge area, such as
a hill or mountain.
Steep topography can also complicate the modeling by
making it more difficult to simulate hydraulic heads
that are representative of the hydrologic units of
interest.
Regional Recharge/Discharge
The ground-water flow paths will largely be controlled
by regional and sub-regional ground-water recharge
and discharge areas. It is generally necessary to ensure
that the conceptual model of flow and transport on a
local scale is consistent with the sub-regional and
regional scale. If the site is located in an aquifer
recharge area, the potential for widespread aquifer
contamination is significantly increased, and reliable
modeling is essential.
3.2.3 Land Use and Demography
The site conceptual model will need to identify the
locations where ground water is currently being used,
or may be used in the future, as a private or municipal
water supply. At sites with multiple user locations, an
understanding of ground-water flow in two or three
dimensions is needed in order to predict realistically
the likelihood that the contaminated plume will be
captured by the wells located at different directions,
distances, and depths relative to the sources of
contamination.
Simple analytical ground-water flow and transport
models typically are limited to estimating the
radionuclide concentration in the plume centerline
downgradient from the source. Accordingly, if it is
assumed that the receptors are located at the plume
centerline, a simple model may be appropriate. Such
an assumption is often appropriate even if a receptor is
not currently present at the centerline location because
the results are generally conservative. In addition, risk
assessments often postulate that a receptor could be
located directly downgradient of the source at some
time in the future.
The need for complex models increases if there are a
number of public or municipal water supplies in the
vicinity of the source. Under these circumstances, it
may be necessary to calculate the cumulative
population doses and risks, which requires modeling
the radionuclide concentrations at a number of specific
receptor locations. Accordingly, off-centerline
dispersion modeling may be needed.
3-5
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SECTION 4
CODE SELECTION - RECOGNIZING IMPORTANT MODEL CAPABILITIES
The greatest difficulty facing the investigator during the code selection process is not determining which codes have
specific capabilities, but rather which capabilities are actually required to support remedial decision making during
each remedial phase at a specific site. This section is designed to help the remediation manager and support personnel
recognize the conditions under which specific model features and capabilities are needed to support remedial decision
making.
4.1 INTRODUCTION
The influence that site and code related characteristics
have on code selection can be both global in nature as
well as very specific and exacting. For this reason, this
section is divided into two distinct parts. The first part
addresses general considerations of the code selection
process. The discussion provides an overview of how
the code selection process is influenced by the
interdependency between the modeling objectives and
the site and code characteristics. The second part of
the section focuses primarily on specific considerations
related to the code selection process. The discussion
provides the information necessary to determine which
specific site characteristics need to be explicitly
modeled and when attempting to model such
characteristics is impossible, unjustified, or possibly
even detrimental to the modeling exercise.
4.2 GENERAL CONSIDERATIONS - CODE
SELECTION DURING EACH PHASE IN
THE REMEDIAL PROCESS
Successful ground-water modeling must begin with the
selection of a computer code that is not only consistent
with the site characteristics but also with the modeling
objectives, which depend strongly on the stage of the
remedial process; i.e., scoping vs. site characterization
vs. the selection and implementation of a remedy.
There are no fail-safe methods for selecting the most
appropriate computer code(s) to address a particular
problem. However, the entire process of code selection
can be relatively straightforward if it is given adequate
attention early in the project development.
One of the primary goals of mathematical modeling is
to synthesize the conceptual model, as discussed in
section 3, into mathematical expressions, which, in
turn, are solved by selecting an appropriate computer
code. This section discusses how the different
components of the conceptual model, in conjunction
with the modeling objectives, influence the modeling
approach and ultimately the selection of the most
appropriate computer code.
The underlying premise of this section is that the
various aspects of the conceptual model may be
simulated in a variety of ways, but the selected
approach must remain consistent with the objectives.
That is, the physical system cannot be overly
simplified to meet ambitious objectives, and less
demanding objectives should not be addressed with
sophisticated models.
Table 4-1 presents an overview of how the overall
approach to modeling a site differs as a function of the
stage of the remedial process. The most common code
selection mistakes are selecting codes that are more
sophisticated than are appropriate for the available
data or the level of the result desired, and the
application of a code that does not account for the flow
and transport processes that dominate the system. For
example, a typical question that often arises is: when
should three-dimensional codes be used as opposed to
two-dimensional or one-dimensional codes? Inclusion
of the third dimension requires substantially more data
than one- and two- dimensional codes. Similar
questions need to be considered which involve the
underlying assumptions in the selection of a modeling
approach and the physical processes which are to be
addressed. If the modeler is not practical,
sophisticated codes are used too early in the problem
analysis. In other instances, the complexity of the
modeling is commensurate with the qualifications of
the modeler. An inexperienced modeler may take an
unacceptably simplistic approach.
4-1
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Table 4-1. General Modeling Approach as a Function of Project Phase
Attributes
Accuracy
Temporal Representation of
Flow and Transport Processes
Dimensionality
Boundary and Initial
Conditions
Assumptions Regarding Flow
and Transport Processes
Lithology
Methodology
Data Requirements
Scoping
Conservative
Approximations
Steady-State Flow and
Transport Assumptions
One-Dimensional
Uncomplicated
Boundary and Uniform
Initial Conditions
Simplified Flow and
Transport Processes
Homogeneous/Isotropic
Analytical
Limited
Characterization
Site-Specific
Approximations
Steady-State Flow/Transient
Transport Assumptions
1 ,2-Dimensional/Quasi-
3 -Dimensional
Non-Transient Boundary
and Nonuniform Initial
Conditions
Complex Flow and
Transport Processes
Heterogeneous/Ani so tropic
Semi-Analytical/Numerical
Moderate
Remediation
Remedial Action Specific
Transient Flow and
Transport Assumptions
Fully 3-Dimensional/Quasi-
3 -Dimensional
Transient Boundary and
Nonuniform Initial
Conditions
Specialized Flow and
Transport Processes
Heterogeneous/Ani so tropic
Numerical
Extensive
One should begin with the simplest code that would
satisfy the objectives and progress toward the more
sophisticated codes until the modeling objectives are
achieved.
The remedial process is generally structured in a way
that is consistent with this philosophy; i.e., as the
investigation proceeds, additional data become
available to support more sophisticated ground-water
modeling. The data that are available in the early
stage of the remedial process may limit the modeling
to one or two dimensions. In certain cases, this may be
sufficient to support remedial decision making. If the
modeling objectives cannot be met in this manner,
additional data will be needed to support the use of
more complex models. The selection of more complex
models in the later phases often depends on the
modeling results obtained with simpler models during
the early phases.
Generally in the later phases of the investigation,
sufficient data have been obtained to meet more
ambitious objectives through complex three-dimen-
sional modeling. The necessary degree of sophistica-
tion of the modeling effort can be evaluated in terms of
both site-related issues and objectives, as well as the
qualities inherent in the computational methods
available for solving ground-water flow and transport.
Modeling objectives for each stage of the remedial
investigation must be very specific and well defined
early within the respective phase of the project. All too
often modeling is performed without developing a
clear rationale to meet the objectives, and only after the
modeling is completed are the weaknesses in the
approach discovered.
The modeling objectives must consider the decisions
that the model results are intended to support. The
selected modeling approach should not be driven by
the data availability, but by the modeling objectives
which should be defined in terms of what can be
accomplished with the available data. It is important
to keep in mind that the modeling objectives should be
reviewed and possibly revised during the modeling
process. Furthermore, ground-water modeling should
not be thought of as a static or linear process, but
rather one that must be capable of continuously
adapting to reflect changes in modeling objectives,
data needs, and available data.
A final consideration, true for all phases of the project,
is to select codes that have been accepted by technical
experts and used within a regulatory context.
The following discusses computer code selection
during each phase of the remedial process. The
emphasis is placed on the processes and assumptions
inherent in the mathematical models used in computer
codes. The discussion is organized according to the
factors delineated in Table 4-1.
4-2
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4.2.1 Scoping
In the scoping phase, site-specific information is often
limited. Therefore, the modeling performed during the
early planning phase of most remedial investigations
is generally designed to support relatively simple
objectives which can be easily tied to more ambitious
goals developed during the later phases of the
investigation. The very nature of the iterative process
of data collection, analysis, and decision making
dictates that the preliminary objectives will need to
evolve to meet the needs of the overall program. That
is, it would be unreasonable to assume that simplified
modeling based upon limited data would do little more
than provide direction for future activities.
An important issue that often arises during the scoping
phase is whether remediation and decommissioning
strategies can be selected during the scoping phase
using limited data and simple screening models. Such
decisions can be costly at complex sites where the
nature and extent of the contamination and transport
processes are poorly understood. How-ever, at
relatively simple sites, early remediation decisions can
be made, thereby avoiding the unneces-sary delays and
costs associated with a possibly pro-longed site
characterization and modeling exercise.
A large part of code selection in the early phase of the
investigation is understanding the project decisions
that need to be made, and, of these, which can be
assisted through the use of specific codes under the
constraints of both limited data and an incomplete
understanding of the controlling hydrogeologic
processes at the site. It is not always necessary to
select a computer code or analytical method that is
consistent with all aspects of the conceptual model. It
is often useful to model only certain components of the
conceptual model. In practice, early modeling focuses
upon assessing the significance of specific parameter
values and their effects on flow and transport rather
than modeling specific hydrogeologic transport
processes. For instance, it is common during the
scoping phase to evaluate transport as a function of a
range of hydraulic conductivities; however, it is
unlikely that more complex processes such as flow and
transport through fractures would be considered.
Because general trends, rather than accuracy, are most
important during the scoping phase, a computer code
or analytical method would need to be capable only of
accommodating the following:
! Conservative Approximations
! Steady-State Assumptions
! Restricted Dimensionality
! Uncomplicated Boundary and Initial
Conditions
! Simplified Flow and Transport Processes
! System Homogeneity
These model attributes generally translate to modeling
approaches that are consistent with the available data
during the scoping phase. They are discussed in
greater detail in the following sections.
4.2.1.1 Conservative Approximations
In the scoping phase of the investigation, the objectives
are generally focused on establishing order of
magnitude estimates of the extent of contamination
and the probable maximum radionuclide
concentrations at actual or potential receptor locations.
At most sites, the migration rates and contaminant
concentrations are influenced by a number of
parameters and flow and transport processes which
typically would not have been fully characterized in the
early phase of the investigation. The parameters
include recharge, hydraulic conductivity, effective
porosity, hydraulic gradient, distribution coefficients,
aquifer and confining unit thicknesses, and source
concentrations. Questions during the early phases
regarding flow and transport processes are typically
limited to more general considerations, such as
whether flow and transport are controlled by porous
media or fractures and whether the wastes are
undergoing transformations from one phase to another
(e.g., liquid to gas).
One of the most useful analyses at this point in the
remedial program is to evaluate the potential effects of
the controlling parameters on flow and transport. One
objective of the early analyses is to assess the
relationship among the parameters. How do changes
in one parameter affect the others and the outcome of
the modeling exercise? A better understanding of such
interdependencies would assist in properly focusingthe
site characterization activities and ensuring that they
are adequately scoped. Obviously, it would also be
desirable to evaluate the effects that various processes
4-3
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would have on controlling flow and transport;
however, this would generally have to be deferred until
additional information is obtained during site
characterization. Furthermore, some caution is needed
in that if simplistic assumptions have been made in the
model, the results may not be valid (i.e., transferable)
to a more refined model that incorporates more
realistic or complex boundary conditions, initial
conditions, or parameter variations.
In general, the uncertainty associated with each of the
parameters is expressed by a probability distribution,
which yields a likely range of values for each
parameter of interest. At this phase in the remedial
process, it is important to select a modeling method
where individual parameter values can be
systematically selected from the parameter range and
easily substituted into the governing mathematical
equations which describe the dominant flow and
transport processes at the site. In this manner, the
effects that a single parameter or a multitude of
parameters have on the rate of contaminant movement
and concentrations may be evaluated. This technique
of substituting one value for another from within a
range of values is called a sensitivity analysis. It is
important to ensure that the range of individual
parameter values and parameter combinations selected
allow for a conservative analysis of the flow and
transport processes.
In many cases, the possible range of values of
important parameters is unknown or very large. As a
result, the analyst has little alternative but to evaluate
the sensitivity of the results to a very broad range of
possible values for the parameters. Many of these
results will be unrealistic but cannot be ruled out until
reliable site data are obtained during site
characterization. These types of analyses are useful
because they help to direct the field work. However,
they can also be used incorrectly. For example,
individuals not familiar with the scoping process could
come to grossly inappropriate conclusions regarding
the potential public health impacts of the site based on
the results of scoping analyses. Accordingly, care
must be taken to assure that the results of scoping
analyses are used to support the decisions for which
they were intended.
An alternative to the detailed sensitivity analysis is a
conservative bounding approach. In this less
demanding analysis, values are selected from the
parameter range to provide the highest probability that
the results are conservative, i.e., that the contaminant
migration rates and concentrations would not be
underestimated. For example, high values of hydraulic
conductivity combined with low effective porosities
and distribution coefficients would tend to maximize
the predicted contaminant migration rates although the
concentrations at receptors may be underestimated.
It is important to keep in mind that even though efforts
are made to ensure a conservative analysis, a number
of natural as well as anthropogenic influences may
adversely affect the migration of radionuclides. For
instance, distribution coefficients that are published in
the literature are frequently determined at neutral pH
values. However, even values conservatively selected
from the low range could be too high if acid wastes
have been discarded with the radioactive material.
Burrowing animals and construction activities have
also been responsible for moving radioactive wastes
beyond the boundaries predicted by ground-water flow
and transport models.
Other processes that could render an otherwise
conservative analysis with erroneously optimistic
results include facilitative transport and discrete
features, such as soil macropores. Facilitative
transport is a term used to describe the mechanism by
which radionuclides may couple with either naturally
occurring material or other contaminants and move at
much faster rates than would be predicted by their
respective distribution coefficients. Furthermore,
discrete features are rarely considered in early
analyses, even though it is well known that discrete
features, such as soil macropores, can allow
contaminant movement on the order of meters per year
in the vadose zone. The result could be a gross
underestimate of the time of arrival and concentration
of contaminants downgradient. Nonetheless, the lack
of site-specific data will generally preclude the
mathematical modeling of anomalous flow and
transport processes during the project scoping phase.
Therefore, the potential exists that what would
normally be considered conservative modeling results
are actually underestimating the contaminant velocities
and concentrations. This possibility highlights the
need for confirmation of modeling results with site-
specific field data even if a conservative approach has
been undertaken.
As far as code selection is concerned, three basic
choices are available: analytical, semi-analytical, or
numerical codes (Appendix C). Analytical and semi-
4-4
-------
analytical methods, which are limited to simplified
representations of the physical setting and flow and
transport processes, are ideally suited for performing
sensitivity and conservative bounding analyses because
they are computationally efficient (i.e., fast) and
require relatively little data as input (Section 4.3.2.1).
Several analytical models are set up specifically for
performing sensitivity analyses.
In contrast, numerical methods do not lend themselves
to the same kind of "simplified" applications. The
primary reasons are that numerical models are difficult
to set up, require a large amount of data input to
calibrate the model, and multiple parameter
substitutions are generally very cumbersome.
However, the bottom line is that simply not enough
data exist in the early phases of a remedial project to
construct and perform defensible numerical modeling.
4.2.1.2 Steady-State Solutions
In the scoping phase, the data that are generally
available have been collected over relatively short time
intervals. Therefore, modeling objectives would be
limited to those which could be met without a detailed
understanding of the temporal nature of processes
affecting flow and transport. For example, a typical
analysis that would not require detailed knowledge of
the temporal nature of recharge, source release rates,
and other flow and transport mechanisms would be the
estimation of the distance that radionuclides have
traveled since the beginning of waste management
activities. This analysis would use yearly average
values for the input parameters, such as ambient
recharge, stream flow stages, and source concentration
release rates. However, without accommodating the
transient nature of these processes, predictions of peak
contaminant concentrations arriving at downgradient
receptors would be associated with a high degree of
uncertainty.
Analytical transport solutions are generally able to
simulate only systems that assume steady-state flow
conditions, but, because the available data rarely
support transient simulations during the scoping
phases, common analytical methods may oftenbe used
more effectively than numerical methods. It is much
easier to conduct bounding and sensitivity analyses
with analytical rather than numerical models.
4.2.1.3 Restricted Dimensionality
Ground-water flow and contaminant transport are
seldom constrained to one or two dimensions.
However, during scoping, modeling objectives must
take into account that there is rarely sufficient
information to describe mathematically the controlling
flow and transport processes in three dimensions. In
reality, most of the modeling analysis in the
preliminary investigation will focus upon centerline
plume concentrations which are essentially one- and
two-dimensional analyses. One-dimensional analyses
of the unsaturated zone are customarily performed in
a cross-sectional orientationbecause flow and transport
are predominantly vertically downward. Similarly, in
the saturated zone, vertical gradients are generally
much smaller than lateral gradients and, as a result,
vertical transport need not always be explicitly
modeled. Therefore, two-dimensional areal analyses
may be appropriate.
Figures 4-1 through 4-4 may be useful in visualizing
the differences between one-, two-, and three-
dimensional modeling. In one-dimensional modeling,
the radionuclide concentration is predicted in the
plume centerline in the x direction, and no information
is provided on the radionuclide concentration in the y
or z direction (Figure 4-1).
Figure 4-1. One-Dimensional Representation of
Conceptual Model
4-5
-------
In two-dimensional cross-sectional models for the
unsaturated zone, the radionuclide concentration is
calculated for the x and z direction and it is assumed
to be the same at any slice through the plume in the y
direction (Figure 4-2).
Figure 4-2. Two-Dimensional Cross-Sectional
Representation of Unsaturated Zone in
Conceptual Model
In saturated zone area! models, the radionuclide
concentrations are predicted for the x andy directions,
but it is assumed the radionuclide concentration is the
same in any slice in the z direction (i.e., the
concentration at any location is the same at all depths)
(Figure 4-3).
X^ -^"
/ " / ^^if J..-"'
' i ,-" ~sy
rVrV-^
Figure 4-3. Two-Dimensional Area!
Representation of Saturated Zone
Conceptual Model
Cross-sectional modeling of the saturated zone in
which flow is assumed to be in the lateral and vertical
directions (e.g., transverse flow is ignored) may also be
performed. A quasi-three-dimensional modeling
approach is also commonly used when vertical
components of flow within aquifers are deemed
unimportant. This approach assumes that ground-
water flow through any confining units that separate
aquifers is in only one dimension (i.e., vertical).
Furthermore, flow within the aquifers is two
dimensional (i.e., vertical flow component is ignored).
In this manner, the effects of the hydraulic
interconnection among interbedded aquifers and
confining units canbe simulated without having to rely
on fully three-dimensional models.
Three-dimensional models will calculate the
radionuclide concentrations at any x, y, z coordinate,
taking into consideration the variations in the
lithography and hydrogeology in three dimensions
(Figure 4-4).
v
,.-"
\-S//t
..'**' f
X ^ / /
.«". _x
i ^ $\S /
-*. -.-' * --x^
***4* "S°"x.^'""" ,,-f* "% ./ ;
^ « ? *
Figure 4-4. Three-Dimensional Representation of
Conceptual Model
A typical three-dimensional problem would be one
which would be designed to evaluate the geometry of
hypothetical capture zones if one or more extraction
wells were planned for the remediation of the ground
water. The vertical ground-water gradient that would
be artificially created by the pumping wells, as well as
the induced vertical leakage from overlying and
underlying hydrogeologic units, would be very
important to consider in this analysis. If this leakage
were not accounted for, the effectiveness of the
remedial system would be substantially overestimated
4-6
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because the radii of the capture zones would be too
large.
As a general rule, analytical methods, which can be
performed on a hand-held calculator, are developed for
predicting concentrations along the centerline of the
plume and are limited to one dimension. Two- and
three-dimensional analyses are customarily performed
with the assistance of a digital computer. Although
analytical solutions are available for two- and three-
dimensional analysis, the limitations that are placed
upon the solution techniques are so severe that they
can be used only to simulate gross system behavior.
Therefore, the three-dimensional example provided
above could not be satisfactorily addressed by an
analytical model because of computational limitations,
such as simple boundary conditions and uniform
geology. However, attempts to circumvent the
limitations of analytical methods at this phase by
adopting numerical methods would only complicate
the problem for reasons previously discussed, as well
as now having to provide parameter estimates in the
second or third dimension.
At this phase, the question is not really whether to use
analytical or numerical methods but rather how many
dimensions should be included in the analytical
modeling. The advantages of adding a second or third
dimension must be carefully weighed against the
further complications of performing the sensitivity
analysis which provides the real strength behind the
application of analytical methods.
4.2.1.4 Uncomplicated Boundary and Uniform
Initial Conditions
Boundary conditions are the conditions the modeler
specifies as known values in order to solve for the
unknowns in the problem domain (Figure 4-5).
Ground-water boundaries may be described in terms of
where water is flowing into the ground-water system
and where water is flowing out. Many different types
of boundaries exist, including: surface water bodies,
ground-water divides, rainfall, wells, and geologic
features such as faults and sharp contrasts in lithology.
Initial conditions are defined as values of ground-water
elevation, flow volumes, or contaminant
concentrations which are initially assumed to be
present in the area of interest.
Governing equations that describe ground-water flow
and contaminant transport and associated boundary
and initial conditions may be solved either analytically
or numerically. Analytical solutions are preferable
because they are easily adapted to sensitivity analyses;
however, in most cases, analytical methods are not
possible because of irregularly shaped boundaries and
heterogeneity of
Ji
^ \ v-,,7;;
^^A^f^-x
f/ -
, f ' t*iir-'
ff
" I
f t 1
Figure 4-5. Typical System Boundary Conditions
4-7
-------
both the geology and flow field. If very few data are
available for the site, it would be very unlikely that
reliable ground-water elevations and flow volumes
could be assigned to calculate the unknowns in the
domain of a numerical model. Furthermore, the
boundary conditions in the numerical model are not
supposed to be subject to radical adjustments and are
generally excluded from detailed sensitivity analyses.
In contrast to numerical methods, analytical methods
are conducive to testing and evaluating both the
boundary and initial conditions. In fact, analytical
methods do not require that boundary values be known
and assigned for the planes and surfaces that surround
the modeled region. However, this is also a limitation
of analytical methods in that, if boundary conditions
vary within the problem domain, they cannot be
adequately simulated.
The lack of site-specific data available in the scoping
phase will generally not allow a good definition of the
system boundary and initial conditions; therefore, the
objectives will be confined to very limited calculations
of approximate travel distances and contaminant
concentrations.
Most analytical models will not accommodate non-
uniform boundary or initial conditions. Therefore, if
the domain includes areas where recharge is variable
or a lake or stream exhibits strong effects on the flow
field, analytical modeling will not provide good
agreement with the overall system behavior. It follows
that, if the flow field is uniform, which can generally
be described with simple uniform boundary conditions,
analytical models provide a better method for testing
the boundary conditions than do numerical methods.
However, the true nature of the flow field cannot be
determined until the site is characterized.
4.2.1.5 Simplified Flow and Transport Processes
Site-specific information describing the flow and
transport processes which dominate the migration of
radionuclides would not be available before detailed
site characterization activities are conducted.
Therefore, modeling objectives would need to be
defined as those that could be addressed with only
limited knowledge of the site hydrogeology and
geochemistry. In practice, this means that uniform
porous media flow would be assumed, and that all of
the geochemical reactions that affect the radionuclide
transport would be lumped together as a single
parameter termed the distribution coefficient.
However, the effects of dilution due to the lateral
spreading of the plume over a uniform flow field can
be considered as well as the radionuclide half-lives.
Discrete features, such as macropores, fractures, and
faults, would generally have to be neglected for the
flow and transport analysis, and distribution
coefficients would be selected from literature values
judged to be conservative. Movement through the
unsaturated zone would be simulated with simplified
versions of more complex equations describing the
unsaturated flow and transport.
Unless there were sufficient data to prove to the
contrary, it would be assumed that the flow field was
uniform, and, at this time, there would be few
advantages to selecting a numerical model over an
analytical one. Analytical methods do exist that
describe the flow and transport of radionuclides
through fractures. However, the fracture-flow
modeling would have to be performed as a sensitivity
analysis, as the information to adequately describe the
geometry of the fractures would seldom be available
before site characterization.
4.2.1.6 Uniform Properties
Homogeneity describes a system where all of the
characteristics are uniform within the aquifer, whereas
isotropy means that the hydraulic properties are
identical in all directions. A homogeneous system may
have anisotropic flow properties, if, for example, an
otherwise homogeneous sandstone aquifer has a
greater hydraulic conductivity in the horizontal
direction than in the vertical. Therefore,
hydrogeologic units may have anisotropic qualities but
still be considered uniform throughout, provided the
anisotropy does not vary within the unit.
Prior to site characterization, only the most general
assumptions may be made regarding the relative flow
properties of the aquifers. For example, as a rule of
thumb, it is often assumed that the hydraulic
conductivity in the horizontal direction is ten times
greater than that in the vertical direction for
sedimentary deposits.
Except for some radial flow problems, almost all
available analytical solutions belong to systems having
a uniform steady flow. This means that the magnitude
and direction of velocity throughout the system are
invariable with respect to time and space, which
4-8
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requires the system to be homogeneous and isotropic
with respect to thickness and hydraulic conductivity.
Therefore, analytical methods will not allow the
simulation of flow and transport through layers of
aquifers and aquitards. Furthermore, if there is a
divergence from these uniform properties within the
aquifer, such as direction flow properties of buried
stream channels, analytical models would be unable to
simulate the effect that these features would have on
flow and transport. However, it is unlikely that this
detailed information would be available prior to the
site characterization program.
4.2.2 Site Characterization
The primary reasons for ground-water modeling in the
site characterization phase of the remedial process are
to: (1) refine the existing site-conceptual model; (2)
optimize the effectiveness of the site characterization
program; (3) support the baseline risk assessment; and
(4) provide preliminary input into the remedial
approach. To accomplish these goals, it is generally
necessary to apply relatively complex ground-water
models to simulate flow and transport in the saturated
zone and, in many instances, the unsaturated zone.
A properly designed site characterization program will
expand the data base to enable very specific and often
demanding objectives to be addressed. To meet the
more rigorous requirements, the simplified modeling
approaches undertaken in the scoping phase give way
to more sophisticated means of data evaluation.
However, this added sophistication and heightened
expectations also convey far more complications in
selecting the proper modeling approach. As discussed
previously, the two general types of modeling options
that could be selected during the site characterization
program include analytical and numerical modeling
methods.
In many instances, several different modeling
approaches will be taken to accomplish the objectives
at a particular phase in the investigation. For example,
the output of analytical modeling of the unsaturated
zone, in the form of radionuclide concentrations at the
interface between the saturated and unsaturated zone,
may be used as input to numerical models of the
saturated zone. It must always be kept in mind that,
regardless of the phase of the remedial process, the
simplest modeling approach that meets the modeling
objectives should be taken.
The site characterization program is the first time in
the investigation where flow and transport processes
are identified and investigated. Prior to site
characterization activities, the investigator could only
evaluate the effects of various parametervalues onflow
and transport. In the scoping phase, the modeling
focuses on parameter estimations rather than on the
effects that geochemical and physical flow mechanisms
could have on the fate and transport of contaminants.
Examples of these mechanisms include processes
related to fractures, density dependence, phase
transformations, and changes in the geochemical
environment.
It is important during the site characterization to gain
an appreciation for the governing geochemical
processes, as these reactions may have a significant
impact on the transport of contaminants and can be
simulated indirectly in the analysis by assuming a
specified amount of contaminant retardation. Direct
means (computer codes) for simulating geochemical
processes are available; however, a detailed discussion
of these methods is beyond the scope of this report.
As additional data are acquired during the site
characterization program and abetterunderstanding of
the hydrogeology is achieved, the modeling approach
and code selectionbecome more involved. Without the
data limitations that constrained the choice of methods
to those of an analytical nature in the scoping phase,
the number of possible alternatives in the modeling
approach and code selection process increases
significantly.
Rather than examine many of the available computer
codes and their inherent limitations and capabilities,
the following discussion addresses the rationale for
adopting a modeling approach that will be consistent
with the objectives. This is important because it is
relatively easy to determine the various attributes of the
existing computer codes; however, it is far more
difficult to understand the relevance of these attributes
as they apply to a specific site and the modeling
objectives.
The following subcategories, keyed to Table 4-1, are
analogous to those presented in the scoping phase.
Because the modeling objectives of the site
characterization phase differ from those of the scoping
phase, the approach to modeling is also different.
4-9
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Basically, analytical methods will be replaced by
numerical methods in order to use less restrictive and
more realistic assumptions. The following discussions
provide an overview of the concepts, terminology, and
thought processes necessary to facilitate the model and
computer code selection process. The modeling
approach in the site characterization program will
generally be based upon the following:
! Site-Specific Approximations
! Steady-State Flow/Transient Transport
! Multi-Dimensional
! Constant Boundary and Non-uniform Initial
Conditions
! Complex Flow and Transport Processes
! System Heterogeneity
Obviously, if the site characterization activities
discover that the system is very simple and the
objectives can be addressed with analytical modeling,
an approach similar to that outlined in the scoping
phase can be taken.
4.2.2.1 Site-Specific Approximations
In the scoping phase of the investigation, the data
limitations impose a simple modeling approach
which uses conservative parameter estimates. One of
the primary objectives of the site characterization
program is to obtain sufficient data to enable the
conservative modeling approach to be replaced by a
defensible and more realistic approach which
incorporates site-specific data.
Many of the objectives defined for the site
characterization phase of the investigation cannot be
met solely with conservative analyses. If parameter
values are not known, it may be necessary to make
conservative estimates; however, the implications that
a conservative approach may have on other aspects of
the remedial program must also be considered. For
example, if, during the baseline risk assessment,
conservatively high hydraulic conductivities are used
in order to ensure that the downgradient contaminant
arrival times are not underestimated, several problems
may occur. First, it would be difficult to calibrate the
model to known parameters (e.g., potentiometric
surface), and adjustments to other parameters wouldbe
required in order to match measured field values. The
end result would be a model that poorly predicts
system responses to hydraulic stresses (e.g., extraction
wells). A second problem would involve contaminant
concentrations. A conservative increase in hydraulic
conductivity would predict more ground-water flow
through the system than is actually occurring and may
underestimate the contaminant concentrations at
downgradient receptors. Furthermore, problems may
arise during the remedial design. If the modeling
results are used to estimate clean-up times, the model
may predict that water and contaminants are flowing
faster than they actually are and at lower
concentrations. This would result in an underestimate
of both the amount of time required for remediation as
well as the contaminant breakthrough concentrations.
The major impact that the formulation of a more
specific site-conceptual model will have on the
modeling approach is that now parameter ranges have
been narrowed by additional data acquisition, and
sensitivity analyses can become more focused. This
parameter value refinement diminishes the need to
perform a multitude of sensitivity analyses. In
conjunction with the increased demand to more
accurately simulate the controlling flow and transport
processes, the primary advantages of analytical models
are superseded by their inability to simulate more
complex conditions. Therefore, the model selection
process is reduced to determining which numerical
model will best suit the objectives.
4.2.2.2 Steady-State Flow/Transient Transport
The data obtained during the site characterization
program are generally collected over relatively short
time intervals and frequently do not reflect the
temporal nature of the hydrogeologic system.
Unfortunately, objectives that need to be addressed
during the site characterization phase often involve the
prediction of temporal trends in the data. For instance,
the risk assessment would generally include an
analysis of the peak arrival times of radionuclides at
downgradient receptors. This incompatibility between
the objectives and data availability gives rise to some
of the greatest uncertainties associated with the entire
remedial investigation. However, one of the principal
utilities of mathematical models is their ability to
extrapolate unknown values through time.
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The modeling approach during site characterization
will generally assume a steady-state flow field and
accommodate the transient nature of the system
through the contaminant transport analysis. Steady or
transient leaching rates would be used in conjunction
with the existing plume concentrations for initial
conditions. Therefore, the system is actually modeled
as a steady flow system and possibly a transient or
pulse-like source term. However, the transient nature
of the plume is generally used as a model calibration
parameter and is not carried forward into the
predictive analysis for future radionuclide
concentrations. That is, rarely are there sufficient data
to describe the temporal nature of the source release.
Exceptions to this are when records are available
pertaining to the volumes of radioactive liquids that
were dumped over time into absorption trenches or
when correlations between rainfall events and source
leaching rates may be extrapolated.
Analytical methods are able only to simulate systems
that assume steady-state flow conditions, although
some analytical codes will allow for the simulation of
a transient source term. Therefore, analytical methods
can be used to simulate the temporal nature of the
contaminant plumes to predict probable maximum
concentrations and contaminant arrival times.
However, other limitations within the analytical codes
often preclude their use during the site characterization
phase.
Almost all of the numerical transport codes written for
radioactive constituents are able to simulate constant
radionuclide source terms with radioactive decay.
However, if the simulation of a pulse-like source term
is desired, special care is needed to ensure that this
capability has been written into the code. Otherwise,
the source release would have to be manually
simulated using a code that models a single pulse in an
iterative fashion for each separate pulse.
4.2.2.3 Multi-Dimensional
The site characterization program should be designed
to gather sufficient data to develop a three-dimensional
conceptual model. It is only after the three-
dimensional system is relatively well understood that
it can be determined whether one-, two-, or three-
dimensional modeling is necessary. If one or two
dimensions are eliminated from the analysis, careful
consideration needs to be given to what impact
restricting the dimensions will have on the model's
capability to simulate existing field conditions.
The magnitude of flow and transport in any direction
relative to the other directions provides the rationale
for which dimension(s) should be included or
excluded. In most instances, flow and transport in the
unsaturated zone are assumed to be predominantly
downward with smaller horizontal components. If the
flow components are found to have two dominant flow
directions, a two-dimensional cross section may allow
a representation of the flow field.
Modeling and field validation studies of the vadose
zone (the unsaturated zone) have yielded mixed results
both in model calibration and in the comparison of
transport predictions against measured field values. In
modeling the vadose zone, as well as the saturated
zone, the question is always how much uncertainty in
the results is acceptable to meet the objectives.
Two-dimensional simulations of the saturated zone are
usually performed when the horizontal flow
components are far greater than the vertical flow
components, allowing the vertical components to be
ignored. However, much of the modeling performed
for site characterization will be on a scale where the
vertical components of flow are usually important
because many natural features, such as surface water
bodies, often have strong vertical flow components
associated with them. Furthermore, particular care
must be taken in eliminating the third dimension
because attempts to simulate three-dimensional
processes in two dimensions can lead to difficulties in
model calibration as well as in producing defensible
modeling results.
Water-level data collected from closely spaced wells
that penetrate the same aquifer at different depths
provide excellent information on the vertical gradients.
This information may be used during the site
characterization program to determine the effective
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hydraulic basement of any contamination present, as
well as recharge and discharge areas. If there are
strong vertical gradients, the capability to simulate the
vertical movement of ground water within the
hydrogeologic system becomes very important in
defining the nature and extent of the contaminant
plume.
It should also be kept in mind that two-dimensional
planar modeling will average the contaminant
concentrations over the entire thickness of the aquifer,
and the vertical definition of the contaminant plumes
will be lost. This vertical averaging of contaminants
will result in lower downgradient concentrations and
may not support a base-line risk assessment. Again,
this example illustrates that the decision on how many
dimensions to include in the modeling must be tied
back to the objectives and the need to be aware of the
limitations imposed upon the results if one or more
dimensions are eliminated.
The recent development of more sophisticated pre- and
post-processors greatly facilitate data entry and
processing. These advances, in conjunction with the
rapid increase in computer speeds over the past several
years, have greatly reduced the time involved in
performing three-dimensional modeling. In general,
there are far more concerns associated with
constraining the analysis to two dimensions than
including the third dimension, even if many of the
parameters in the third dimension have to be
estimated.
Two-dimensional analyses during the site
characterization program are most valuable for
modeling the unsaturated zone and for performing
sensitivity analyses of selected cross-sections through
a three-dimensional model. Two-dimensional
approaches are also useful for performing regional
modeling from which the boundary conditions for a
more site-scale modeling study may be extrapolated.
The objectives for most characterization programs will
be met only by modeling approaches and models that
are multi-dimensional. Analytical models do exist that
are two- and three-dimensional, but they have very
little versatility and would rarely suffice in meeting
complicated objectives. Furthermore, the likelihood
that analytical methods could be effectively used in the
remedial design and evaluation are even more remote.
Therefore, numerical methods should almost always be
chosen if detailed analysis is required to meet the site
characterization objectives.
There are numerous two- and three-dimensional flow
and transport codes to describe the saturated zone.
However, only a handful of three-dimensional codes
exist that describe flow and transport through the
unsaturated zone. A number of codes exist that are
generally three-dimensional; however, certain
transport properties (e.g., dispersion) within these
codes are simulated in only two dimensions. Special
attention should be given to ensure that the controlling
flow and transport processes are described in the
number of dimensions desired to meet the objectives.
Code selection should not only take into account the
required dimensionality of the site characterization
analysis, but also the projected modeling needs of the
remedial design and evaluation phase. It is much
easier to use a code with three-dimensional capability
for a two-dimensional analysis and later expand to the
third dimension than it is to set up a three-dimensional
code from output obtained from a separate two-
dimensional model.
4.2.2.4 Constant Boundary and Non-uniform
Initial Conditions
In general, boundary conditions are known or
estimated values that are assigned to surfaces and
planes that either frame the perimeter of the modeled
area or define the nature of release from the
contaminant source. The different types of flow
boundary conditions are: (a) head (ground-water
elevation) is known for surfaces or planes bounding the
modeled region; (b) ground-water flow volumes are
known for surfaces or planes bounding the modeled
region; (c) some combination of (a) and (b) is known
for surfaces or planes bounding the region. Boundary
conditions could also be assigned to interior features of
the modeled region where ground-water elevations or
flow volumes are known, such as lakes, rivers or
marshes.
The most common contaminant-source type boundaries
either specify the source concentration or prescribe the
mass flux of contamination entering the system. The
concentration is generally prescribed when the release
rate is largely controlled by the solubility limits of the
contaminant. The mass flux type boundary is typically
used when a leaching rate is known or estimated.
Specialized source boundaries have also been
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formulated which allow the source to radioactively
decay. The ability of the code to treat source decay
may not be important if the parents and daughters have
a relatively long half-life when compared to the
expected travel time to the nearest receptor.
One of the primary objectives of the site
characterization program is to identify the presence
and location of ground-water flow and contaminant
source boundaries so that they may be incorporated
into the conceptual model. These boundaries are
generally quantified in terms of the volume of ground
water and contamination moving through the system.
The physical boundaries are then translated into
mathematical terms as input into the computer model.
Initial conditions are defined as values of ground-water
elevation, flow volumes or contaminant
concentrations, which are initially assigned to interior
areas of the modeled regions. At least for the flow
modeling performed during the site characterization,
the initial conditions are generally set to uniform
values. This is because the temporal nature of the flow
system is usually poorly defined. In addition, if the
flow analysis is performed to steady-state, which is
usually the case, the initial conditions assigned to the
model domain are irrelevant as identical solutions will
be reached for these values regardless of the values
initially assigned. This occurs because these steady-
state values are solely dependent on the values
assigned to the boundaries of the model.
Non-uniform initial values (i.e., contaminant
concentrations) are routinely used in the contaminant
transport analysis to depict the geometry and varying
contaminant concentrations within plume, as well as to
define the contaminant concentrations leaching from
the contaminant source. The ability of a code to allow
non-uniform initial conditions would be essential to
fully describing and simulating the contaminant
plume(s).
Analytical models are written for very specific
boundary conditions and uniform initial conditions. In
essence, this means that the boundary conditions
cannot vary spatially and, in most instances, only one
type of boundary condition can be accommodated.
Furthermore, analytical methods do not allow for the
contaminant source concentrations to change through
time and the measured plume values (i.e., non-uniform
initial conditions) cannot be input directly to the
model. Understandably, these restrictions would
impose significant limitations on analyzing the data
collected during the site characterization program.
Numerical models are broadly designed to adapt to
many different types of boundary geometries and
initial conditions. Non-uniform initial conditions for
a single contaminant plume can almost always be
varied spatially, depending upon the dimensionality of
the code.
The ability of numerical models to handle complex
boundaries and non-uniform initial conditions bestow
a versatility to the analysis which should be compatible
with the objectives. This approach is consistent with
the principles behind coupling the sophistication of the
modeling with that of the existing knowledge base.
4.2.2.5 Complex Flow and Transport Processes
Site-specific information describing the flow and
transport processes which dominate the migration of
radionuclides would not have been available during the
scoping phase of the investigation. As the site
characterization activities progress, greater attention is
focused upon the physical, chemical, and biological
processes that are affecting ground-water flow and
contaminant transport. Up until this time, the
attention has been placed primarily upon estimating
parameter ranges and variances within these ranges
via the sensitivity analyses. This approach has
limitations and needs to be broadened during the site
characterization phase if ground-water flow and
contaminant transport are to be well described. The
means by which this parameter-based approach is
expanded is by using computer codes that
mathematically accommodate the dominant flow and
transport processes. These processes could include
flow and transport through fractures, density-driven
flow, matrix diffusion, fingering, surface water/ground
water interactions, and geochemical reactions. If
present, each of these processes can invalidate the
output of models that are based on the assumption that
uniform flow and transport are occurring through a
homogenous porous media.
It is still likely that all of the geochemical reactions
that affect the radionuclide transport would be lumped
together into the single parameter termed the
distribution coefficient. However, a better delineation
of any geochemical facies would allow for the
distribution coefficient to vary from layer to layer as
well as within the units themselves. If this simplified
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means of simulating geochemical processes is found to
be inadequate, it may be necessary to utilize
geochemical models in order to explicitly address
specific geochemical reactions by relying upon
thermodynamically based geochemical models.
Movement through the unsaturated zone could be
simulated in a number of different ways depending
upon the objectives. If the unsaturated zone is
relatively thin and travel times are short, it may be that
simplified versions of more complex equations
describing the unsaturated flow and transport would
suffice. However, if the travel time through the
unsaturated zone is significant and accurate flow and
transport predictions are required, then mathematical
methods, which account for complex processes
associated with flow and transport through the
unsaturated zone, may be necessary.
The modeling obj ectives need to be defined prior to the
characterization; only in this fashion can it be assured
that data are sufficient to perform modeling at the
necessary level of complexity. All too often,
limitations within the data, rather than the modeling
objectives, drive the sophistication of the modeling.
Analytical methods are not well suited to simulate
complex flow and transport processes. Further, even
numerical methods do not satisfactorily describe some
flow and transport processes. These processes include
facilitative transport and non-Darcian flow, which are
discussed in section 4.3.
4.2.2.6 System Heterogeneity
One of the primary objectives of the site
characterization program is to identify heterogeneity
within the system and to delineate zones of varying
hydraulic properties. System heterogeneity is one of
the leading causes of a poor understanding of the
physical system controlling flow and transport.
If the accurate simulation of heterogeneous rocks is
required to meet the modeling objectives, analytical
methods would be inappropriate as they assume the
rocks to all have the same properties. In contrast, most
numerical codes allow for zones with different porous
rock properties; however, relatively few codes can
simulate discrete features, such as faults, fractures,
solution features, or macropores. Numerical codes
vary from one another in their ability to simulate sharp
contrasts in rock properties. For example, many codes
would have a problem arriving at a solution (i.e.,
convergence) if very impermeable rocks dissected
highly permeable rocks. Therefore, if the site was
situated in an alluvial flood plane bordered by low
permeability bedrock, special care would be needed to
select a code that will not have numerical convergence
problems caused by permeability contrasts.
In selecting a computer code to be applied during the
site characterization, consideration should also be
given to what scenarios may be modeled during the
remedial investigation. If a low-permeability slurry
wall or sheet pile cut-off walls may be installed, it
would be important that the computer code be able to
simulate these features through permeability contrasts.
4.2.3 Remedial Phase
As the site investigation proceeds into the remedial
phase, data are acquired that will assist in the
identification of feasible remedial alternatives. These
data, in combination with models, are used to simulate
the flow and transport in support of the selection,
design, and implementation of the remedial
alternatives. The data and models are used to predict
the behavior of ground-water flow and the transport of
radionuclides and thereby aid in the selection and
design of the remedy and demonstrate that the selected
remedy will achieve the remedial goals.
The modeling objectives associated with remedial
alternative design are generally more ambitious than
those associated with the site characterization phase of
the remedial process. Therefore, it is often necessary
either to select a computer code with more advanced
capabilities, or modify the existing model in order to
simulate the more complex conditions inherent in the
remedial design. The following are specific examples
of processes that may not be important to the baseline
risk assessment and site characterization, but are often
essential to the remedial design:
! three-dimensional flow and transport;
! matrix diffusion (pump and treat);
! desaturation and resaturation of the aquifer
(pump and treat);
! heat-energy transfer (in-situ vitrification/
freezing);
! sharp contrasts in hydraulic conductivity
(barrier walls);
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I
multiple aquifers (barrier walls);
i
! the capability to move from confined to
unconfined conditions (pump and treat); and
ability to simulate complex flow conditions
(pumping wells, trenches, injection wells).
From a modeling standpoint, the remedial design is the
most challenging phase of the remedial investigation.
Frequently, it is the first time in the process that
sufficient data are available to enable the model
predictions to be verified. The very nature of many of
the potential remedial actions (e.g., pump and treat)
provide excellent information on the temporal response
of the flow and transport to hydraulic stresses. These
data allow continuous refinement to the calibration and
enable the model to become a very powerful
management tool.
The following describes modeling during the remedial
phase of the investigation. The modeling approaches
taken at various sites would generally have the
following characteristics in common:
! Remedial Action Specific
! Transient Flow and Transport
! Multi-Dimensional
! Prescribed Boundary and Non-uniform
Initial Conditions
! Specialized Flow and Transport Processes
! System Heterogeneity
4.2.3.1 Remedial Action Specific
As the site characterization process comes to an end
and the Remedial Design and Selection Phase is
entered, data have been acquired which will define the
remedial alternatives. The various remedial
alternatives can be conveniently grouped into the
following three categories:
! Immobilization
! Isolation
! Removal
This section briefly describes each category, the types
of processes that need to be modeled to support each
category, and the special information needs for each of
these categories. The information is required not only
for implementation of the remedial design but also to
evaluate its effectiveness through numerical modeling.
Immobilization
Immobilization of the radioactive wastes refers to
physical, chemical, and/or biological processes used to
stabilize the radionuclides and preclude their transport.
A number of treatment options exist, each having their
own associated modeling needs, including:
! Physical
vapor extraction
in-situ coating
grouting of fissures and pores
in-situ freezing
in-situ vitrification
! Chemical
induce secondary mineralization
induce complexation
alter oxidation-reduction potential
! Biotic
in-situ microbial activity
! Physical/Chemical
alter surface tension relationships
alter surface charges
in-situ binding
adsorbent injection
radionuclide particle size augmentation
through clay flocculation
The following are the types of physical, chemical, and
biological processes that may need to be modeled to
support alternative remedies based on immobilization:
! Physical Properties and Processes
unsaturated zone flow and transport
heat energy transfer
multiple layers
vapor transport
extreme heterogeneity
temperature-dependent flow and
transport
! Chemical Properties and Processes
density-dependent flow and transport
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oxidation-reduction reactions
system thermodynamics
chemical speciation
ion-exchange phenomena
precipitation
natural colloidal formation
radiolysis
organic complexation
anion exclusion
! Biotic Properties and Processes
biofixation
It would be ideal if these processes and properties
could be reliably described and modeled with
conventional and available models. However, many of
these properties and processes are not well understood,
and, in these instances, models do not exist that yield
reliable results.
The specialized data required to support ground-water
modeling of immobilization techniques include:
! Determination of temperature-dependent
flow and transport parameters
! Characterization of geochemical
environment
! Determination of the alteration of the
physical rock properties that govern flow and
transport
! Characterization of the microbial
environment
Isolation
A common remedial alternative is to emplace
protective barriers either to prevent contaminated
ground water from migrating away from a
contaminated site or to divert incoming (i.e., clean)
ground water from the source of contaminants.
Several types of materials are being used to construct
suchbarriers, including soil andbentonite, cement and
bentonite, concrete, and sheet piling. An alternative to
the physical emplacement of protective barriers is the
use of hydraulic containment which involves
controlling the hydraulic gradient through the use of
injection and/or withdrawal wells or trenches in order
to contain and treat the contaminant plume. Examples
of potential barriers include the following:
! Physical
hydraulic containment
grout curtains, sheet piling, bentonite
slurry walls
low permeability caps (clay and/or
synthetic)
! Chemical
ion-exchange barriers
! Biotic
microbial barriers
If properly designed and emplaced, such barriers can
last for several decades, barring any geological
disturbances, such as tremors, ground settling,
significant changes in hydraulic gradients, etc.
Accordingly, suchbarriers can be useful in mitigating
the impacts of relatively short-lived radionuclides, or
to control the migration of long-lived radionuclides
until a more permanent remedy can be implemented.
Several mechanisms or processes can affect the long-
term integrity of such barriers. Once the installation
is complete, failures can be due to cracking,
hydrofracturing, tunnelling and piping, and chemical
disruption. Changes in the site's geological or
hydrological characteristics can also lead to
catastrophic failures, such as partial collapse, settling,
and breaking. If a barrier should fail following
installation, water may infiltrate the site, and
contaminated leachates may move beyond the site.
This type of failure could result in the dispersion of
contaminants in the environment.
The modeling approaches that would be consistent
with simulating the effects that flow barriers would
have on the fate and transport of radionuclides are
closely tied to the ability of the code to accommodate
a number of factors, including: high permeability
contrasts, transient boundary conditions, and possibly
chemical and biological reactions. These
considerations will be discussed in greater detail in the
following sections.
The following are the types of physical, chemical, and
biological processes that may need to be modeled to
support alternative remedies based on isolation. Many
of these processes are very complex, and attempts at
modeling will meet with varying degrees of success:
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! Physical Properties and Processes
unsaturated zone flow and transport
runoff
multiple layers
vegetative cover
transient source term
extreme heterogeneity
areal recharge and zero flux capability
! Chemical Properties and Processes
localized ion exchange phenomena
! Biotic Properties and Processes
localized biofixation
microbial population modeling
Typical characterization data needs related to barrier
emplacement include:
! Barrier dimensions
! Barrier hydraulic conductivity
! Geochemical environment
! Structural integrity of barrie^arrier
degradation
! Microbial environment
! Detailed hydrogeology
! Physical
soil excavation (solid)
pump and treat (vapor)
in-situ vaporization (liquid)
! Biotic
injection and removal of biomass foam
The following are the types of physical, chemical, and
biological processes that may need to be modeled to
support alternative remedies based on removal. Most
of these processes and properties are readily described
in mathematical terms and can be modeled relatively
reliably. Obviously, modeling the biological activity
associated with the injection of a biomass will have the
same limitations that are common to other types of
biological modeling.
! Physical Properties and Processes
transient source term
unsaturated zone flow and transport
matrix diffusion
desaturation and resaturation of the
aquifer
vapor transport
! Biotic Properties and Processes
physical injection and withdrawal of the
biomass
microbial population modeling
Typical characterization needs related to radionuclide
removal include:
Removal
Radioactively contaminated soil can result from the
disposal of both solid and liquid waste. Solid wastes
may have been buried in the past without sufficient
integrity of containment so that, eventually,
radioactivity intermingled with the contiguous soil.
Percolation of rain water through shallow burial sites
can contribute further to the migration of radionuclides
to lower depths as well as to some lateral movement.
Wider areas of contamination have occurred when
waste, stored temporarily at the surface, has lost
containment and has been disbursed by the wind. The
technologies that are most commonly applied to
remove solid, liquid, and vapor (e.g., tritium)
radionuclides include the following:
! Air permeability of the unsaturated zone
! Unsaturated zone flow and transport
parameters
! Areal extent of contaminated wastes
! Depth to ground water
! Saturated zone flow and transport properties
The degree to which these factors are addressed in the
modeling relies heavily upon the objectives as well as
the availability of the required data. Specific examples
of how these considerations are tied into the modeling
approach are provided in the sections that follow.
4.2.3.2 Transient Solutions
The data that are available by the time the remedial
design phase is entered usually span a relatively long
time frame, which often allows the temporal nature of
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the hydrogeologic system to be relatively well defined.
If this is the case, the remedial design objectives could
involve many criteria that could not have been met
during the modeling activities in the site
characterization phase. Many of these additional
criteria of the design phase objectives may require that
the code have the capability to perform transient flow
and transport simulations. This capacity would be
necessary to evaluate the effectiveness of a number of
remedial alternatives. One such alterna-tive would be
the placement of earthen covers and a broad range of
natural and synthetic barriers, which are engineered to
establish a cap over surface and subsurface soil. One
of the objectives of the cover is to prevent rainwater
from percolating through contaminated soil and
carrying radionuclides to the ground water. In the site
characterization program, the objectives were such that
they could probably have been met by assuming
constant areal recharge over the modeled area.
However, this steady-state approach would not account
for recharge rates which vary through time, which
would be needed to simulate the deterioration of the
cap and the subsequent effect on the radionuclide
leaching rates.
Soil excavation of radioactively contaminated soil will
result in some amount of residual radioactivity
remaining in the soil contiguous to the removal
operations. It could also result in the redistribution of
contaminants in the unsaturated zone. Without the
ability to perform transient simulations, with the
source now largely removed, it would not be possible
to determine how long it would take for the remedial
actions to have a noticeable effect on downgradient
receptors.
4.2.3.3 Multi-Dimensional
The need to perform three-dimensional modeling
during the remedial phase will largely depend upon
what remedial alternatives are under consideration and
how the effectiveness of the selected alternative will be
evaluated.
The remedial alternatives that are most commonly
supported by three-dimensional and quasi-three-
dimensional modeling are those that impart a strong
artificial stress to the hydraulic flow field, such as
pumping wells and extraction trenches. Under many
circumstances, the vertical ground-water gradients,
prior to these imposed stresses, would be several orders
of magnitude less than the horizontal gradients and,
therefore, could be ignored in a one- or two-
dimensional flow analysis. However, when the
hydraulic gradients are significantly altered by
imposed stresses, three-dimensional flow fields
generally develop. Without the capability to simulate
the actual flow field in three dimensions, it would be
very difficult to effectively determine capture zones
and influent contaminant concentrations. This is
largely because vertical leakance from units above and
below the screened interval of the extraction well
would be ignored as well as vertical concentration
gradients.
Another remedial alternative that generally creates
three-dimensional flow fields are physical barriers to
ground-water flow. Whether the barriers consist of
grout injection techniques, sheet pile cutoff walls, or
bentonite slurry walls, all of these procedures will have
a common problem which is that the hydraulic head
will build up behind the structures and induce vertical
gradients allowing ground water to flow under the
barriers. In these cases, the analysis of vertical flow is
essential in determining probable leakage rates and the
volume of water that would potentially flow through
the structure.
4.2.3.4 Transient Boundary and Non-Uniform
Initial Conditions
Most of the modeling analysis up until the remedial
phase can be performed with constant boundary
conditions. This means that physical features within
the modeled area, such as the water elevations of
surface water bodies and areal recharge, can be
simulated with values that remain constant with time.
Once the remedial phase is reached, however, the
modeling objectives may require that the transient
nature of these boundaries are incorporated into the
analysis, and time-weighted averages may no longerbe
applicable. For instance, water bodies, such as
radioactively contaminated waste lagoons, would
probably have been treated as constant boundaries
during the site characterization modeling, and their
water-surface elevations would have been held
constant. However, if one of the remedial activities
involved withdrawing contaminated water from one or
more of the lagoons, the effect that the change in
water-surface elevations would have on the ground-
water gradients could be evaluated only by simulating
the drop in surface elevations through time. This
would be done by prescribing the boundaries of the
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lagoon(s) to change with time in order to simulate the
expected extraction rates.
The ability to prescribe boundaries within the model
would also be important in the evaluation of in-situ
soil flushing techniques, which are used to enhance the
mobility of contaminants migrating towards recovery
points. In this case, recharge would be varied through
time to reproduce the effects that various rates of
flushing would have on the ground-water flow and
contaminant transport.
Protective barriers to ground-water flow are
constructed of very low permeability material and
emplaced either to prevent contaminated ground water
from migrating away from a site or to divert incoming
clean ground water from the source of contaminants.
If properly designed and emplaced, barriers to flow can
last for several decades, barring any geological
disturbances, such as tremors, ground settling,
significant changes in hydraulic gradients, etc.
However, if a barrier should fail following installation,
water may infiltrate the site, and contaminated
leachates may move beyond the site. Therefore, the
effects that the failure of a barrier would have on
contaminant flow and transport should be evaluated
through modeling. There are a number of ways that
the failure of the barrier could be simulated. The most
straightforward method is to use transient boundaries
to simulate additional flow through the barrier as well
as a reduction in the difference between water-level
elevations in front and behind the barrier. Therefore,
a code selected for this simulation should have the
capability to incorporate transient boundaries.
4.2.3.5 Specialized Flow and Transport Processes
The design and evaluation of remedial alternatives
frequently involve the consideration of flow and
transport processes that were probably not explicitly
modeled during the site characterization program.
These processes include: complex geochemical
reactions, matrix diffusion, heat flow, and possibly
biological reactions.
As mentioned previously, numerical models that
satisfactorily couple ground-water flow and
contaminant transport to complex geochemical
reactions simply do not exist. The complex
geochemical models are based upon the laws of
thermodynamics, which means that they predict
whether the potential exists for a particular reaction to
occur within a closed system. Despite many
shortcomings inherent within the methods for
analyzing complex geochemical reactions, it is
important that the controlling geochemical reactions
be examined, possibly in laboratory benchscale or field
studies. This is particularly important when
physical/chemical stabilization processes are under
consideration whereby physical or chemical agents are
added to, and mixed with, a waste (typically sludge in
pits, ponds, and lagoons), with the objective of
improving the handling or leaching characteristics of
the waste destined for land disposal.
A detailed understanding of the geochemistry can also
be very useful in estimating leach rates for uranium
mill tailings which otherwise would be associated with
possibly unacceptably high uncertainties.
Matrix diffusion is the process by which concentration
gradients cause contaminants either to move into or be
drawn out of low-permeability rocks where diffusion
governs contaminant transport rather than advection
and dispersion. Pump and treat systems will tend to
draw water from the more permeable units, which may
leave large volumes of contaminants stored in the clays
and otherfine-grained materials, which will eventually
diffuse out. Many computer codes do not adequately
simulate this very slow process. If matrix diffusion is
not accounted for, the contaminant movement will be
based solely upon ground-water velocities rather than
the diffusion term. Ground-water velocity will
generally move the contaminant much more rapidly
than diffusion, and clean-up times may be dramatically
underestimated.
In-situ vitrification (ISV) of soils is a thermal
treatment and destruction process that achieves
stabilization by converting contaminated soil and
wastes into chemically inert, stable glass and
crystalline products, resembling obsidian. Predicting
the effectiveness of IS V and its implementability would
require a number of specialized processes to be
modeled. One such process would be vapor transport
of radionuclides, such as tritium, which would be an
important health consideration if the media were to be
heated.
A mechanism that appears to affect the transport of
radionuclides under some conditions is microbial
fixation. Radionuclides may be immobilized and/or
mobilized by organisms or plants. Immobilization
may occur if radionuclides are incorporated in the cell
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structure of microorganisms or plants that are
relatively stationary. On the other hand, radionuclides
may be mobilized by forming biocolloids withbacteria,
spores, and viruses. Modeling of microbial processes
requires a code that, at a bare minimum, allows a
degradation rate to be assigned to the contaminant(s).
4.2.3.6 System Heterogeneity
The ability of a code to accommodate severe contrasts
in soil and rock properties is particularly important
during the design and evaluation of physical barriers
for protecting ground water. If the application
involves extending the barrier down to a low
permeability strata to form a seal and deter underflow
leakage, it would be important that the code allow the
incorporation of multiple stratigraphic layers as well as
sharp hydraulic conductivity contrasts. Only in this
manner could the effect on contaminant flow and
transport due to the effects of leakage through the
barrier wall and basement strata be evaluated.
4.3 SPECIFIC CONSIDERATIONS
The purpose of this section is to guide the Remediation
Manager and support personnel in determining what
specific capabilities are needed from a computer code
to address the modeling objectives. The discussion
focuses on explanations as to how specific site and
code characteristics will provide the information
necessary to decide whether various code attributes
could potentially assist in the analysis or be
detrimental to the analysis, or whether they are simply
unnecessary.
After the conceptual model is formulated and the
modeling objectives are clearly defined in terms of the
available data, the investigator should have a relatively
good idea of the level of sophistication that the
anticipated modeling will require. It now becomes
necessary to select one or more computer code(s) that
have the attributes necessary to describe
mathematically the conceptual model at the desired
level of detail. This step in the code selection process
requires detailed analysis of the conceptual model to
determine the degree to which specific waste and site
characteristics need to be explicitly modeled.
Fundamental questions that need to be answered at this
stage in the code selection process are presented in
Table 4-2. In answering these questions, the
investigator must decide whether a particular code has
the required capabilities and the importance of
individual aspects of the conceptual model in the
modeling analysis. It is generally relatively
straightforward to ascertain whether a code has a
specific capability, and many documents are already
available which provide this kind of information. It is
far more difficult to decide whether or not a certain
attribute of a model is needed to accomplish the
modeling objectives. Furthermore, other factors must
be considered in the code selection process which are
independent of the waste, site characteristics, and
modeling objectives. These factors are inherent in the
individual computer codes and include: solution
methodology, availability of the code, hardware
requirements, usability of the code, and the degree to
which the code has been tested and accepted.
Accordingly, this section has two goals:
1. to describe the detailed waste and site
characteristics and flow and transport processes
that may need to be explicitly modeled in order to
achieve the modeling objectives, and
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Table 4-2. Questions Pertinent to Model Selection
Site-Related Features of Flow and Transport Codes
Source Characteristics
Does the contaminant enter the ground-water flow system at a point, or is it distributed along a line or
over an area?
Does the source consist of an initial pulse of contaminant, is it constant over time, or does it vary over
time?
Is the contaminant release solubility controlled?
Soil/Rock Characteristics
Are anisotropy and heterogeneity important?
Will fractures or macropores influence the flow and transport?
Are discrete soil layers relevant to the analysis?
Aquifer System Characteristics
What type of aquifers does the model need to simulate? Confined, unconfined, or both?
Does the model need to simulate complete dewatering of a confined aquifer?
Does the model need to simulate aquitards?
Does the model need to simulate the dewatering and resaturation of an aquifer?
Do multiple aquifers need to be accounted for?
Transport and Fate Processes
Which transport and fate processes need to be considered in the analysis (e.g., retardation, chain decay
reactions, matrix diffusion)?
Multiphase Fluid Conditions
Are all of the wastes miscible in water?
Is the gas phase important to the analysis?
Are density effects important?
Flow Conditions
Will flow be under fully saturated or partially saturated conditions?
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Table 4-2. (Continued)
Code-Related Features of Flow and Transport Codes
Time Dependence
Are the fluctuations in the hydrogeologic system significant, requiring transient analyses, or can they be
ignored and simulated as steady state?
Solution Methodology
How will the various mathematical methods used to solve the flow and transport equations affect the
model results and therefore code selection?
What will be the hardware requirements?
Code Geometry
In how many dimensions is the code capable of modeling the representative flow and transport processes?
Source Code Availability
Is the code publicly available?
If not, how much does it cost and is the source code available?
Code Testing
Has the code been verified?
Has the code been field-validated?
Has the code been independently peer reviewed?
Code Input and Output
What input data parameters are required?
Does the code have a pre- or post-processor?
Will the code provide breakthrough curves?
How will the output depict plume extent?
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2. to describe the characteristics inherent in a
computer code that could influence the practical
usefulness of the code, including the usability of
the code and the extent to which the code has been
tested.
Once these two objectives are accomplished, the code
selection process becomes simply identifying the codes
that meet the modeling needs.
In light of these goals, this section is divided into two
parts, one addressing the site-related characteristics
and the other addressing code-related characteristics
that must be considered when selecting a code. Table
4-3 presents a matrix relating various site
characteristics and an example of codes that explicitly
model those characteristics. Table 4-4 presents a
matrix relating various code characteristics and an
example of codes that have those characteristics. The
following sections discuss the conditions and
circumstances under which the various characteristics
are important.
Referring to Tables 4-3 and 4-4, it is not the intention
of this section to construct comprehensive reference
tables listing all available codes, but rather to provide
tables that clearly illustrate the criteria generally
considered in the identification of candidate computer
codes. Each of the criteria is discussed individually in
context to its relevance in answering the questions
identified in Table 4-2.
Once one or more computer code(s) are identified as
potential candidates, the codes should undergo further
review as a cross-check to ensure that the code has the
capabilities that are specified in the literature.
Furthermore, a more detailed review can provide
valuable insight into the nuances of the code which are
generally not available from cursory code reviews.
4.3.1 Site-Related Characteristics
The general components of the conceptual model that
need to be considered when selecting an appropriate
computer code are the following:
! Source Characteristics
! Aquifer and Soil/Rock Characteristics
! Transport and Fate Processes
! Fluid Conditions
! Flow Conditions
Each of these topics is presented as a major heading in
Table 4-3. These broad subjects are further divided
into their individual components both in the table and
in the discussion that follows.
The objective of the subsequent presentation is not only
to discuss the relevance that each of the site- related
characteristics may have to the code selection process,
but also to provide criteria to determine whether a
particular attribute of a code will be important in the
analysis.
4.3.1.1 Source Characteristics
The accurate portrayal of the contaminant source term
is one of the most difficult tasks in the modeling
process. All too often there is a general lack of data
that characterize the nature and extent of the
contamination as well as the release history. Computer
codes can accommodate the spatial distribution of the
contaminant source in several ways. The most
common are the following:
! Point source
! Line source
! Area! source
Each of these source types can have an associated
release mechanism in which either the mass flux or
concentration is specified. The two general types of
source-term boundary conditions include the
following:
! Concentration is prescribed
! Contaminant mass flux is prescribed
Source Delineation
The determination of how the spatial distribution of
the source term should be modeled (i.e., point, line, or
area) depends on a number of factors, the most
important of which is the scale at which the site will be
investigated and modeled. If the region of interest is
very large, when compared with the contaminant
source area, even sizable lagoons or landfills could be
considered point sources.
Typically, a point source is characterized by
contaminants entering the ground water over a very
small area relative to the volume of the aquifer (e.g.,
injection well). Line sources are generally used
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Table 4-3. Site-Related Features of Ground-Water Flow and Transport Codes
Section 4.3.1.1 Source Characteristics
Point Source
Line Source
Areally Distributed Source
Multiple Sources
Specified Concentration
Specified Source Rate
Time-Dependent Release
Section 4.3.1.2 Aquifer and Soil/Rock Characteristics
Confined Aquifers
Confining Unit(s)
Water-Table Aquifers
Convertible Aquifers
Multiple Aquifers
Homogeneous
Heterogeneous
Isotropic
Anisotropic
Fractures
Macropores
Layered Soils
Section 4.3.1.3 Fate and Transport Processes
Dispersion
Advection
Matrix Diffusion
Density-Dependent Flow and Transport
Retardation
Non-linear Sorption
Chemical Reactions/Speciation
Single Species First Order Decay
Multi-Species Transport with Chained Decay Reactions
Section 4.3.1.4 Multiphase Fluid Conditions
Two-Phase Water/NAPL
Two-Phase Water/Air
Three-Phase Water/NAPL/Air
Section 4.3.1.5 Flow Conditions
Fully Saturated
Convertible Aquifers
Variably Saturated/Non-Hysteretic
Variably Saturated/Hysteretic
Section 4.3.1.6 Time Dependence
Steady-State
Transient
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Table 4-4. Code-Related Features of Ground-Water Flow and Transport Codes
Section 4.3.2.1 Geometry
1-D Vertical/Horizontal
2-D Cross Sectional
2-D Area!
Quasi 3-D (Layered)
Fully 3-D
Section 4.3.2.2 Source Code Availability
Proprietary
Section 4.3.2.3 Code Testing and Processing
Verified
Field-Validated
PC-Version 3 86-SR486
Pre and Post Processors
Section 4.3.2.3 Model Output
Contaminant Mass/Rate of Release to Ground Water
Contaminant Plume Extent
Contaminant Concentration as a Function of Distance
As a Function of Depth from Surface
Continuously Distributed in Space
Average at Selected Points or Cells
Profiles at Selected Points Over Time
Appendix C Solution Methodology
Analytical
Approximate Analytical
Exact Analytical
Semi-Analytical
Numerical
Spatial Discretization
Finite Difference
Integrated Finite-Difference
Finite Element
Method of Characteristics
Temporal Discretization
Explicit
Implicit
Mixed Implicit-Explicit
Matrix Solvers
ADIP
Direct Solution
Iterative ADIP
SOR/LSOR/SSOR
SIP
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when the contaminants are entering the aquifer over
areas where the length of the source greatly exceeds its
width, such as leaking pipes or unlined trenches.
Areal sources are often associated with agricultural
applications of fertilizers and pesticides. Uranium mill
tailings would also frequently be treated as an area!
source for modeling purposes.
In some instances, it may be desirable to model
multiple contaminant source areas. This would be
particularly important if cumulative health effects are
to be determined or if the extent and nature (e.g.,
commingling of various contaminant plumes) of
contamination will have a significant impact on the
remedial design. It is possible, however, to perform
multiple-source modeling with codes that do not
inherently allow the incorporation of multiple sources.
The most common approach to accomplishing this
objective is to perform a series of simulations in which
each model run assumes only one source. The output
from each of the successive model runs is subsequently
cumulated into a representative multiple-source site
model.
The number of dimensions (i.e., one, two, or three)
that will be explicitly modeled will tend to impose
limitations on how a contaminant source can be
modeled.
A point source can be simulated with either a one-,
two-, or three-dimensional model, whereas a line or
areal source must be modeled with either a two- or
three-dimensional model. One-dimensional codes are
constrained to simulating contaminant sources as
points. The following four factors will determine
whether the source should be modeled as a point, line,
or area source:
! Modeling objectives
! History of waste disposal activities
! Distribution of contaminants
! Fate and transport processes
The modeling objectives are probably the single most
important factor in determining the way in which the
source term should be modeled. One-dimensional
simulations of point sources will yield generally
conservative approximations of contaminant
concentrations because of limited dispersion.
Therefore, if the modeling objective is to determine
maximum peak concentrations arriving at
downgradient receptors, area and line sources could be
simulated as point sources comprised of average or
peak concentrations. However, if more realistic values
of concentrations and plume geometry are required, it
will generally be necessary to simulate the source term
characteristics more accurately.
Some knowledge of the history of the waste disposal
activities can often provide valuable insight into the
probable nature of the contaminant source term. In
general, the longer the site has been active, the more
likely it is that the wastes have been dispersed over a
larger area and discarded in many different forms.
The presence of product and waste lines immediately
suggests that line sources are present. Absorptionbeds
and storage tanks indicate potential point sources,
whereas mill tailings, large lagoons, and air emissions
that carried and subsequently deposited contaminants
in the site vicinity would generally represent area
sources.
The distribution of measured contaminants in the soil
and ground water will also provide clues as to the
nature of their source. Contaminants that are wide-
spread and of similar concentrations suggest an area
source, while narrowly defined areas of contamina-tion
indicate a more localized or point source.
Dominating fate and transport processes should also be
considered when assigning source term characteristics.
If flow and transport properties are strongly confined
to one or two dimensions, as in the unsaturated zone
(i.e., liquids flow down vertically due to gravity in the
unsaturated zone), it may be possible to use a more
simplified approximation of the source geometry (e.g.,
point).
Release Mechanism
Computer codes can simulate the introduction of
contaminants to the ground water as an instantaneous
pulse or as a continuous release over time. A
continuous release may either be constant or vary with
time. The two most common means of simulating
continuous or pulse releases are by either specifying
release concentrations or by specifying the
contaminant mass entering the system. In general,
both approaches have drawbacks and limitations and
require considerable thought and possibly a number of
independent calculations prior to selecting and
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implementing the most appropriate method for the
modeling exercise. Furthermore, most ground-water
flow and transport codes do not explicitly account for
the physical degradation of waste containers and,
therefore, anticipated release rates must be estimated
through other means (e.g., waste package codes) and
input as boundary conditions into the flow and
transport model.
It is generally preferable to pose the source-term
release in terms of contaminant mass flux, rather than
specified concentrations. This is true even if the
concentration at the source is known. The primary
problem with specifying the concentration of the
contaminants entering the system is that care must be
taken to ensure that the total mass that enters the
system does not exceed that which would actually be
available from the source. Furthermore, specified
concentrations tend to over-predict contaminant
concentrations near the source because the effects of
dilution and dispersion are not properly accounted for.
However, it is not uncommon for specified
concentrations to be used if the release of the
contaminant is controlled by its solubility limit; that is,
if the contaminant is relatively insoluble. The
rationale for this approach is that specified
concentrations would tend to describe leaching rates
that are solubility controlled.
Not all computer codes allow the concentration or
mass of a continuous release to change with time. This
quality is particularly important if it is suspected that
conditions in the past or future are not approximated
by those of the present. A specific example would be
modeling the performance of an engineered barrier
whose performance is expected to change with time.
Radioactive source terms present special considera-
tions in that the mass fraction of the parent isotopes
will diminish with time due to radioactive decay.
However, if the radionuclide mass release is solubility
controlled, the concentration of the leachate may
remain constant despite the decay of the source term.
The release concentrations may remain constant until
the source term has decayed to concentrations where
solubility limits no longer dictate the amount of
radionuclides that may go into the solution.
Computer codes have been developed that can simulate
single or multiple aquifers which may behave as
confined, unconfined, or change from one condition to
another. Intrinsic characteristics of the aquifers and
aquitards, which control flow and transport, are also
simulated to various degrees by computer codes. The
most common code selection criteria with regard to
aquifers and their characteristics include the following:
! Confined aquifers
! Water-table (unconfined) aquifers
! Multiple aquifers/aquitards
! Heterogeneous
! Anisotropic
! Fractures/macropores
! Layered soils/rocks
Water-Table and Confined Aquifers
The ground water flowing within a water-table aquifer
is in immediate contact with the atmosphere and is
directly recharged through the overlying unsaturated
zone. This water-table surface is equal to atmospheric
pressure and is free to rise and fall within the aquifer
in response to varying amounts of recharge (e.g., rain).
The water-table aquifer generally follows land-surface
topography and is frequently revealed in the form of
surface-water bodies such as lakes and rivers (Figure
4-6).
A confined aquifer is one in which the ground water is
isolated from the atmosphere by some geologic feature
(e.g., confining unit). As a result, the ground water is
under pressure greater than that of atmospheric, and,
if a well penetrates a confined aquifer, the water in the
well will rise above the top of the aquifer.
In most circumstances, the water first encountered
beneath the site will be under water-table conditions.
However, this does not always mean that water levels
measured in wells are indicative of the water-table
4.3.1.2 Aquifer and Soil/Rock Characteristics
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\ r x/
Figure 4-6. Water Table and Confined Aquifers
surface. This discrepancy may occur when a well is
screened below the water table in an unconfined
aquifer with large vertical gradients (or a well with a
very long screen in an unconfined aquifer with large
vertical gradients). In many instances, particularly
with domestic wells, water in the shallow water-table
aquifer has been cased off and a deeper unit, that may
be under confined conditions, is supplying water to the
well. The importance of this is that the water in a well
that taps a confined aquifer can rise significantly
higher in the well than the true water-table surface. If
this is the case, the thickness of the unsaturated zone
may be significantly underestimated.
The mathematical descriptionforground-waterflow in
a water-table aquifer is more complex than that for
flow in a confined aquifer. This is largely because the
saturated thickness of a water-table aquifer will vary
with time and, therefore, the transmissivity (which is
the quantity of volume of water flowing through the
aquifer, mathematically calculated as the product of
the hydraulic conductivity and the vertical thickness of
the aquifer) is also time dependent. Confined aquifers
always remain saturated and, therefore, the
mathematics do not have to account for a varying
transmissivity.
Computer codes that simulate confined aquifers can
also be used to simulate water-table conditions if the
saturated thickness of the aquifer is not expected to
vary by more than ten percent over the time of interest.
This assumption would generally be appropriate if the
modeling objectives can be met by assuming steady-
state conditions. If significant changes (greater than
ten percent) in the water-table elevation are expected
over the time of interest, not only would a steady-state
modeling approach be of uncertain value, but the
validity of applying a computer code designed to
simulate confined flow to problems that involve
unconfined flow would be questionable.
The importance of whether the system is under steady
state or transient conditions dictates that the length of
the time of interest needs to be carefully considered in
context of the code applicability. In general, the
shorter the time of interest the more likely it is that
fluctuations of the water table will exceed ten percent
of the saturated thickness. As the length of the time of
interest increases, long-term averages tend to dampen
out the extremes within the water-table fluctuations.
Examples of conditions where a code developed for
confined conditions would probably not be applicable
to simulate ground-water flow in water-table aquifers
include:
! Highly variable recharge rates
! Ephemeral effects of surface-water bodies
! Remediation activities
!
Physical properties of the contaminants
Shallow ground-water flow systems that are recharged
primarily from percolating precipitation tend to be
strongly influenced by seasonal fluctuations of the
local climate. Summer droughts and spring snow
melts can cause dramatic shifts in the water-table
elevation. For reliable seasonal predictions, computer
codes would have to be able to simulate changes in the
aquifer transmissivity through time. Such is not the
case if the use of long-term recharge averages could be
justified, as when estimating average annual radiation
doses associated with the drinking water pathway.
In many cases, water-table aquifers are closely tied to
surface-water bodies which are ephemeral in nature.
These surface-water bodies may include intermittent
and ephemeral streams, waste lagoons, and tidal
marshes. It is important that the transient effect of
these features on the water table be considered when
selecting an appropriate computer code.
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Remediation activities may also create large
oscillations of the water table. Activities that include
active remediation, such as pump and treat, artificial
recharge, and ground-water injection will generally
have the greatest impact on the ground-water table.
Relatively passive remediation activities, such as
ceasing the disposal of liquids into lagoons or streams,
may also affect the shallow aquifer by causing the
water table to find a new equilibrium which may or
may not be significantly different from the initial
position.
A special consideration for modeling water-table
aquifers, particularly when the aquifer is being
significantly dewatered, as in pump and treat
operations, is that not all computer codes with the
capability to simulate water-table aquifers have the
capacity to resaturate the aquifer if it becomes
completely dewatered. This could pose a serious
limitation if one of the objectives is to evaluate the
effectiveness of a pump and treat system that is
operated intermittently.
In determining whether a computer code that does not
simulate water-table conditions is appropriate, some
consideration needs to be given to the nature of the
contaminants. For example, the flow of LNAPL
(contaminants less dense than water, such as oil) is
complicated by the rise and fall of the water table
within the seasons. As the water table falls, the layer
of mobile contaminant also falls. When the watertable
rises, the contaminant also rises. However, residual
contamination is left behind in the saturated zone. If
the water table rises faster than the contaminant can
rise, "pockets" of free contaminants might become left
below the water table. The flow of water and
contaminants is controlled by Darcy's law and depends
upon the effects of density, viscosity, and relative
permeability. Depending upon these factors, either the
contaminant or the water could have a greater velocity
as the water table rises and falls. Therefore, in order
to predict remediation times accurately, the volume of
the contaminant remaining in the unsaturated zone
needs to be estimated. If the code does not allow the
water table to rise freely within the aquifer, the
interaction between the contaminant and the water
table cannot be simulated.
Relatively few computer codes have been developed
that will simulate conditions within an aquifer that are
changing from confined conditions to water-table
conditions. This capability is particularly useful for
simulating a ground-water system where a confined
aquifer will be heavily pumped and potentially
dewatered.
Multiple Aquifers/Aquitards
Computer codes have been developed that can simulate
either single or multiple hydrogeologic layers (Figure
4-6). Generally, a single-layer code is used if the bulk
of the contamination is confined to that layer or if the
difference of the flow and transport parameters
between the various layers is not significant enough to
warrant the incorporation of various layers.
In deciding whether there is a significant difference in
the flow and transport properties between various
layers, the investigator should keep in mind that the
parameter values that could vary from layer to layer
include: hydraulic conductivity, effective porosity,
distribution coefficients, and bulk densities. In most
instances, effective porosities, distribution coefficients,
and bulk densities are estimated from the literature and
could have a large associated error. Hydraulic
conductivities, which are typically measured in the
field, also may be off by an order of magnitude.
Therefore, it generally does not make much sense to
model discrete layers if estimated parameter values,
separating different layers, fall within probable error
ranges. Furthermore, unless the discrete
hydrogeologic units are continuous over the majority
of the flow path, it is often possible to model the
system as one layer using average flow and transport
properties.
The greater the depth to which the system is modeled,
the more likely it will be that aquifers of varying
characteristics will be encountered. Ideally, the depth
to which the system should be modeled is the depth at
which ground-water gradients become consistently
vertically upward. This depth will define the basement
flow of the shallow system, and most contamination
would be confined to shallower depths unless
contaminants are being driven downward against the
ambient ground-water flow by density gradients.
If very little information is available on the distribution
of vertical gradients, a general rule that is often useful
in estimating the relative base of the flow system is
that discharge areas (e.g., perennial streams, lakes, and
swamps) are associated with upward gradients, while
recharge areas (e.g., mountains and uplands) are
typified by downward gradients. Thus, it is more
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likely that the vertical extent of contamination is
greater when the contaminant source is located in a
recharge area than in a discharge area.
Layered Soils/Rocks in the Vadose Zone
Rarely would soils and rocks within the vadose zone
not exhibit some form of natural layering. The first
consideration as to how this natural layering should be
treated in the modeling analysis is related to whether
the various soil layers have significantly different flow
and transport properties. If these properties do not
vary from layer to layer, then there would be little need
for the code to have multiple-layer capability. On the
other hand, if the layers have distinctive properties that
would affect flow and transport, a decision needs to be
made how best to achieve the modeling objectives; i.e.,
should each layer be discretely treated or should all of
the layers be combined into a single layer?
In most instances, it would be appropriate to combine
the layers into a single layer for all phases of the
remedial program with the following notable
exceptions:
! Vapor-phase transport
! Model calibration
i
Conceptual model development
Vapor-phase transport within the vadose zone, which
can occur with tritiated water vapor, will be largely
controlled by the various flow properties of the soils
within the unsaturated zone. Vapors will tend to
congregate beneath layers with low air permeabilities
and freely move through more permeable layers. The
direction of movement of the vapor is often governed
by the dip and orientation of the soil beds above the
water table and are independent of the ground-water
gradients.
Percolating rainwater may induce a phase-
transformation of radionuclide vapor back to a liquid
phase, thus allowing transport to the saturated zone.
If this process occurs in beds through which
radionuclide vapors have migrated, both away from the
source and up the ground-water gradient, it is possible
that significant amounts of radioactivity may be
detected in the ground-water upgradient of the source
area.
This phenomenon is particularly important to consider
when determining how far upgradient background
monitoring wells should be placed to ensure that the
ambient ground water has not been contaminated via
vapor transport from the contaminant source. In many
systems, with relatively thin vadose zones (< 10 m), it
may be more practical to approach this problem
empirically and simply measure radionuclide vapor
concentrations in the unsaturated zone. However, the
expense of investigating relatively thick vadose zones
(> 50 m) is often significant, and modeling could be
very useful in estimating the likely distance that vapor
may have moved.
An evaluation of expected vapor movement and
concentrations could also be of considerable value
depending upon remedial measure alternatives. For
instance, it may be desirable to predict the potential
movement of vapor out from under a remedial cap or
the movement of water vapor under a capped area.
Without the ability of the code to accommodate
discrete layers, the effect that a low permeability cap
would have on vapor transport could not be simulated.
Under other circumstances, maintenance- related
issues could be addressed, such as the build- up of
hydrogen gas within landfills that contain pyrophoric
uranium (i.e., spontaneously combustible). In landfills
where pyrophoric forms of uranium metal were placed
in drums and submerged in petroleum-based or
synthetic oils to prevent rapid oxidation, there is the
potential for the uranium and petroleum to react to
form hydrogen gas which, at high enough
concentrations, is an explosion hazard.
Models are generally calibrated against measured field
values. However, unless the field characteri-zation
program was designed to characterize the unsaturated
zone, data are frequently insufficient to calibrate a
vadose zone model. Soil sampling would have had to
provide vertical, and in many instances horizontal,
profiles of radionuclide concentrations, soil
permeability, and moisture content data. Therefore, it
is important to decide prior to site characterization
whether a fully calibrated vadose zone transport model
will be required to meet the modeling objectives. After
the characterization is completed, itcanbe determined,
from the data, whether a code is needed that will allow
the simulation of discrete layers.
Calibration of flow and transport through the
unsaturated zone generally becomes important in areas
with relatively thick unsaturated zones (> 100 m). In
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these areas, deep boreholes are both very expensive to
install and difficult to instrument. Under these
circumstances, a calibrated model may be useful in
performing mass-balance calculations to determine the
depth that contaminants could have potentially
migrated, and to provide an estimate of contaminant
volumes requiring remediation.
An accurate portrayal of the site-conceptual model is
essential for all phases of the remedial program. A
computer code with the capability to allow layering
may facilitate the evaluation of various aspects of the
conceptual model. For example, infiltration through
the vadose zone may move laterally over significant
distances, particularly when there are soil layers of low
permeability which impede vertical migration and
allow saturated flow to occur in perched-water zones
(Figure 4-7). This transport process is particularly
important in areas where a relatively thick unsaturated
zone is bisected by deep-cut streams, and the perched
water movement in the unsaturated zone is
predominantly horizontal rather than vertical
infiltration to the water table. Under these
circumstances, the radionuclides may short-circuit the
ground-water pathway and discharge to seeps and
springs along the river wall. Therefore, it could be
important to evaluate the potential for horizontal
movement in the unsaturated zone to ensure that all
exposure pathways are properly accounted for in the
conceptual model.
Anisotropic/Isotropic
In a porous medium made of spheres of the same
diameter packed uniformly, the geometry of the voids
is the same in all directions. Thus, the intrinsic
permeability of the unit is the same in all directions,
and the unit is said to be isotropic. On the other hand,
if the geometry of the voids is not uniform, and the
physical properties of the medium are
""d;..
S....I
Figure 4-7. Perched Water
dependent on direction, the medium is said to be
anisotropic.
Anisotropy can play a major role in the movement of
ground water and contaminants. In most sedimentary
environments, clays and silts are deposited as
horizontal layers. This preferential orientation of the
mineral particles allows the horizontal hydraulic
conductivities to greatly exceed those in the vertical
direction. As a general rule, for sedimentary
environments, it is assumed that horizontal hydraulic
conductivities are 10 to 100 times greater than those in
the vertical direction.
If the modeling analysis does not account for
anisotropy, the contaminants will be predicted to be
more dispersed in the vertical direction than would
probably be occurring in the real world. One of the
primary drawbacks to this taking place is that the
predicted concentrations would be significantly
reduced due to this artificial vertical dispersion and
resulting dilution.
Macropores/Fractures
Modeling flow through the unsaturated zone is based
on the assumption that the soil is a continuous
unsaturated solid matrix that holds water within the
pores. Actual soil, however, has a number of cracks,
root holes, animal burrows, etc., where the physical
properties differ enormously from the surrounding soil
matrix (Figure 4-8). Under appropriate conditions,
these flow channels have the capacity to carry
immense amounts of water at velocities that greatly
exceed those in the surrounding matrix.
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Figure 4-8. Macropores and Fractures
At present, there is no complete theory describing
water flow through these structural voids or
macropores. There is uncertainty regarding the
significance of subsurface voids in water flow, since, if
large, they should fill only when the surrounding soil
matrix is close to saturation. Nonetheless, studies have
shown that contaminants can migrate to substantial
depths with only a small amount of water input.
Many water flow processes of interest, such as ground-
water recharge, are concerned only with areally
averaged water input. Therefore, preferential flow of
water through structural voids does not necessarily
invalidate the code formulations that assume uniform
flow and do not directly account for
macropores. However, preferential flow is of critical
importance in solute transport because it enhances
contaminant mobility and can significantly increase
pollution hazards.
Since codes do not exist that directly simulate flow
through macropores, it is important to select a code
with features that will allow an indirect simulation of
the effects of macropores on flow and transport. A
number of factors should be considered when
determining whether macropores are important in the
modeling analysis, including:
! Presence, geometry, and spatial distribution
of macropores
! Location of the waste relative to
macropores
! Rainfall duration, intensity, and runoff
Determining the presence of macropores may sound
relatively straightforward; however, in many instances,
the formation of macropores is an ephemeral process
where the desiccation and shrinkage of clays will occur
only during the summer months or after long periods
of drought. Therefore, if it is suspected that conditions
are suitable for the formation of macropores, a special
effort should be made to tour the site during the
periods when macropores are most likely to be present.
After establishing the existence of macropores, the
next step would be to gain some understanding of their
geometry and spatial distribution. If macropores are
relatively shallow (< 1 m), it is highly unlikely that
they would have a significant effect on the flow and
transport even if they are closely spaced. However, if
the macropores are relatively deep compared to the
thickness of the unsaturated zone, on the order of ten
percent, their effect on flow and transport should be
considered in the modeling exercise.
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The location of the wastes relative to any macropores
plays a significant role in determining their
importance. Obviously, if the contaminated area is
dissected by numerous relatively deep macropores
extending well below the wastes, it would raise
concerns that flow and radionuclide transport may be
facilitated due to their presence. On the other hand, if
the wastes are buried below the maximum depth of the
macropores, or if the site has been capped or covered
with a material that is not prone to macropore
development, their presence would play a lesser role.
The direct effect that the macropores will have on the
mobility of the wastes is closely tied to whether the
macropores are located beneath the waste. If so, they
may be providing an avenue for radionuclide transport
or, if they terminate above the waste, they may be
indirectly enhancing transport by allowing greater
amounts of recharge to come in contact with the
contaminants.
The rainfall duration, intensity, and runoff also play a
major role in evaluating the relative importance of
macropores on radionuclide transport. If an area is
prone to high-intensity, short-duration storms
(convective precipitation) with low runoff, the rainfall
rates may exceed matrix infiltration rates, and it is not
necessary for the soil to become saturated before water
can flow within the macropores. In this manner, water
and/or contaminants can move well in advance of the
wetting front and be carried beyond the maximum
saturation extent of the soil matrix. In contrast, in an
area which is typically subjected to long-duration
rainfall events with low intensities, it is more likely
that flow will not occur in the macropores but will be
confined to the soil matrix. This is because the soil
matrix infiltration rate will exceed the rainfall rates
characteristic of this cyclonic precipitation.
As mentioned previously, there are no codes that
directly simulate flow and transport through
macropores in the unsaturated zone. Therefore, if it is
determined that macropores are present and may
potentially have an important effect on flow and
transport, several approaches could be used to account
indirectly for the flow and transport within the
macropores. These approaches are based upon the
geometry of the macropores, location of the wastes,
and rainfall characteristics. Each of the approaches
will require a code with the proper attributes, as
outlined below.
If the maximum depth of the macropores is above the
top of the wastes and rainfall occurs at such an
intensity that flow will take place within the
macropores, it will be necessary to evaluate the effect
that additional water reaching the wastes will have on
contaminant transport. To account for this
phenomenon, the code will need the ability to regulate
recharge as well as infiltration rates. More precisely,
the code must be very stable numerically and able to
accommodate areally variable and transient recharge,
anisotropy, and heterogeneity. In essence, higher
recharge rates are applied over short time intervals to
areas of the site with known macropores. However, in
order to enable the soil to absorb the additional water
and to simulate greater infiltration rates, the soil in
this area must also be assigned larger hydraulic
conductivities with high vertical to horizontal ratios.
To handle these sharp soil material contrasts, the code
must be well formulated and not be plagued with
convergence problems (see Appendix C).
In instances where macropores extend beneath the
bottom of the buried wastes, several alternatives exist
for modeling their potential effect on flow and
transport. The most straightforward approach is to
simulate the portion of the macropores that extend
below the wastes by removing an equivalent thickness
from the modeled unsaturated zone. This essentially
assumes instantaneous transport through the
macropores and would result in very conservative
values. This approach has a number of advantages, the
greatest of which is that the computer code does not
need any additional features than it would have
otherwise needed without the macropores. However,
if this approach is thought to be overly conservative,
which would probably be the case if more than half the
thickness of the unsaturated zone would need to be
removed, an alternative could be employed which
involves methods that are used to simulate deep
fractured networks in the vadose zone.
Determining the importance of fractures within the
unsaturated zone generally presents more of a problem
than making the same determination for macropores
because: (1) fractures are usually not visible from the
surface and are difficult to characterize in the
subsurface; (2) if fractures are present, they will often
extend through the entire unsaturated zone and into
the saturated zone; and (3) fractures may serve as
either conduits or barriers to flow. All of these issues
must be addressed in the site characterization program
to determine whether the fractures need to be
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considered in the modeling. In general, fractures that
can be traced through the waste area are important and
should be considered, at least conceptually, in the
analysis.
Fracture modeling of the unsaturated zone can
generally use computer codes with attributes very
similar to those used for modeling macropores with a
few notable exceptions. For the purposes of this
discussion, it is assumed that the fractures are found to
extend through the unsaturated zone into the saturated
zone, and that an assumption of instantaneous flow
through the entire vadose zone thickness would not be
acceptable for the analysis. Unlike macropores, which
will probably not extend to depths greater than 5
meters, fractures may reach depths on the order of
hundreds of meters. This factor has a number of
implications for both the flow of water and transport of
radionuclides.
Rainfall percolating through a fracture will slowly
diffuse into the soil matrix. Thus, eventually the water
moving in the fracture will become so depleted that
fracture flow will no longer develop unless other
sources of water are intercepted (e.g., perched). The
depth at which fracture flow would cease depends on
a number of factors including fracture properties,
rainfall characteristics, and soil matrix qualities, all of
which are closely interrelated and are difficult to
quantify. Conceptually, this process of diffusion into
the matrix at depth suggests a direct correlation
between the importance of the fractures and the depth
of the unsaturated zone. That is, at some depth,
fracture flow will no longer be important.
There will always be a large degree of subjectivity
associated with deciding the importance of fractures'
effects on flow and transport within the vadose zone.
However, it would probably be safe to assume that in
most unsaturated systems, fracture flow below 200
meters is insignificant unless a continuous source of
water is available (e.g., overlying adsorption beds).
The features of computer codes that would be
necessary to describe fracture flow would be similar to
those required to simulate macropores, except that
now, because the pulse-like nature of the recharge
would be dampened at greater depths, it would
probably not be necessary for the code to accommodate
transient recharge, particularly if the depths of interest
are greater than 50 meters. However, the codes must
still be very stable numerically and able to incorporate
anisotropy and heterogeneity, which are discussed in
greater detail in the following sections.
Almost all of the discussion to this point has focused
upon modeling flow and transport in porous media. It
is important to realize, however, that a number of
radioactively contaminated sites overlie areas where
fractures and solution channels are probably dominant
mechanisms for flow and transport. The uncertainty
associated with fracture zone modeling is generally
high, and if fracture modeling is to be successful, a
concentrated effort needs to go into the design of the
field investigation. Therefore, the benefits associated
with modeling fractured flow and transport processes
have to be carefully weighed against a number of
deterrents which include:
! An expanded field program is needed;
! Significant uncertainties are associated with
fracture characterization methods;
! High degree of expertise is required of the
modeler;
! Codes available to simulate fracture flow are
difficult to use.
A number of analytical models are available that do
simulate ground-water flow and radionuclide transport
through fractures. However, it is unlikely that
analytical models could adequately describe flow and
transport processes in most fractured systems because
these processes are much more complex than those in
unfractured granular porous media. This is due to the
extreme heterogeneities, as well as anisotropies, in the
fractured systems. When a radionuclide is introduced
into a fractured porous medium, it migrates through
the fracture openings by means of advection as well as
hydrodynamic dispersion. The radionuclide also
diffuses slowly into the porous matrix. Molecular
diffusion dominates flow and transport within the
porous matrix because the fluid velocity in the porous
matrix is usually very small. Upon introduction of the
radionuclide into a fractured aquifer, the radionuclide
moves rapidly within the fracture network. As time
progresses, the zone of contamination will diffuse
farther into the porous matrix. Since the porous
matrix has a very large capacity to store the
contaminant, it plays a significant role in retarding the
advance of the concentration front in the fractures. If
the source of contamination is discontinued and the
aquifer is flushed by fresh water, the contaminant mass
in the fractures will be removed relatively quickly,
whereas the contamin-ant in the porous matrix will be
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removed very slowly via diffusion back to the fracture
openings.
In general, data limitations and narrow objectives
would preclude the modeling of fractured systems until
at least the Site Characterization phase. If it is
determined that numerical modeling of a fractured
system will be performed during the Site
Characterization, it becomes necessary to evaluate the
data needed to support fracture flow and transport
numerical modeling. In order to adequately
understand the potential data requirements for fracture
flow and transport modeling, the following text
provides a very basic understanding of modeling
fractured systems.
At present there are two general numerical methods for
solving flow and transport in a fractured medium:
modeling of the flow, accounting for the fractures one
by one, or modeling with an equivalent continuous
medium approach.
Flow and transport modeling in a fracture system by a
continuous porous medium approach is performed by
assigning each family of fractures a directional
conductivity, thus constituting a hydraulic conductivity
tensor. As the frequency and direction of these
conductivities are defined, the principal axes of
anisotropy of the tensor and the conductivities in these
directions can be calculated. It is thus assumed that
the fracture spacings are frequent enough that, when
viewed from the perspective of the entire physical
system, flow and transport processes would be
consistent with those associated with porous media.
Therefore, computer codes developed for porous media
may sometimes be used to simulate multiple fracture
families. This approach relies heavily upon the
presence of multiple fractures. However, if there are a
relatively limited number of fractures, as is often the
case with solution channel(s) or faults, an alternative
approach is necessary. This alternative approach
consists of three general methods, which are termed
dual-porosity, dual-permeability, and discrete fracture.
All of these methods need a computer code that is
specifically developed for modeling fracture flow. The
code will have separate equations which are developed
for flow and transport in the rock matrix and are
coupled to equations describing flow and transport in
the fractures. This allows fractures to be assigned flow
and transport properties which are discrete from the
matrix properties. The dual-porosity method assumes
that fractures are relatively uniformly spaced and does
not allow flow to occur among matrix blocks.
Contaminants leave and enter the fractures only
through diffusion. The dual-permeability approach
also assumes that fracture networks are well developed
although this method does allow advective and
dispersive flow through the matrix blocks and is
conducive to simulating highly fractured systems in
which both the matrix and the fractures are relatively
permeable. The discrete fracture approach is similar
to the dual-permeability method although the discrete
fracture method allows single fractures to be modeled
separately as line elements.
In most instances, it is very difficult to obtain the field
data necessary to perform detailed fracture flow and
transport modeling. Such modeling could require a
substantial dedication of resources, and any
commitment should be carefully weighed against that
which may be gained from the modeling.
Circumstances that could lead to a decision to perform
fracture-flow modeling may include:
! Future risks cannot be assessed without
explicitly accounting for flow and transport in
a fractured system;
! Sensitivity or bounding analyses cannot be
designed to meet objectives; and
! Empirical data are either not available or can
not be effectively used to estimate risks,
capture zones, influent concentrations, etc.
Homogeneous/Heterogeneous
A homogeneous unit is one that has the same
properties at all locations. For a sandstone, this would
indicate that the grain-size distribution, porosity,
degree of cementation, and thickness are variable only
within small limits. The values of the transmissivity
and storativity of the unit would be about the same at
all locations. A plutonic or metamorphic rock would
have the same amount of fracturing everywhere,
including the strike and dip of the joint sets. A
limestone would have the same amount of jointing and
solution openings at all locations.
In heterogeneous formations, hydraulic properties
change spatially. One example would be a change in
thickness. A sandstone that thickens as a wedge is
nonhomogeneous, even if porosity, hydraulic
conductivity, and specific storage remain constant.
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Most numerical computer codes have the ability to
assign varying hydraulic conductivities and storage
properties to the hydrostratigraphic units being
simulated. Furthermore, computer codes have also
been developed that have the ability to simulate
constant or variable thicknesses.
Analytical methods are constrained to modeling
aquifers that do not change significantly in thickness
or other aquifer characteristics. Numerical codes may
or may not have been developed for problems
involving an aquifer of variable thickness. Numerical
codes that do not allow the thickness of the aquifer to
vary significantly use transmissivity as the model input
parameter which indirectly describes aquifer thickness
(hydraulic conductivity multiplied by thickness).
However, numerical codes that specify hydraulic
conductivity and aquifer thickness as input parameters
independently calculate aquifer transmissivity
throughout the model domain and, therefore, allow
aquifer thickness to vary. If advective-dispersive
contaminant transport calculations are expected to be
performed at some time in the analysis, it is important
that hydraulic conductivities and aquifer thicknesses
are known even when their product (i.e.,
transmissivity) is only required as model input. This
is because the quantity of ground-water flow through
aquifers of identical transmissivity will be the same
under equal gradients. Therefore, an aquifer which is
very thick and has a low hydraulic conductivity can
have an identical transmissivity to that of another
aquifer which is thin but has a high hydraulic
conductivity. As far as the bulk movement of
groundwater is concerned, the two systems will behave
in a similar fashion when comparative boundary
conditions are applied. However, the transport of
radionuclides would behave very differently within the
two systems, in that velocities would generally be
much greater in systems with higher hydraulic
conductivities.
A few finite-element computer codes use what are
termed curvilinear elements. These are specialized
elements that can be spatially deformed to mimic the
elevations of the upper and lower surfaces of the
hydrogeologic units. Curvilinear elements are
particularly useful when aquifers and aquitards have
highly variable thicknesses.
In general, if it is expected that the aquifer thickness
will vary by more than ten percent, it is recom-mended
that the computer code be capable of simulating
variable thicknesses. If a code does not properly
simulate the aquifer thicknesses, the contaminant
velocities will be too large in areas where the
simulated aquifer is thinner than the true aquifer
thickness and too small in those regions that have too
great a simulated thickness.
The ability to simulate aquifer heterogeneities may also
be very important during the remedial design phase of
the investigation. If engineered barriers of low
permeability are evaluated as potential remedial
options, it would be necessary to determine their
overall effectiveness. In this scenario, it would be
important not only to select a computer code that can
simulate highly variable hydraulic conductivities, but
also to ensure that the sharp contrasts in hydraulic
conductivities do not cause instabilities in the
mathematical solutions.
4.3.1.3 Transport and Fate Processes
The transport of radionuclides by flow through either
a porous matrix or a fractured system will, in each
case, be affected by various geochemical and
mechanical processes. Among the chemical processes
are adsorption on mineral surfaces (both internal and
external to the crystal structure), including the kinetics
of adsorption, and processes leading to precipitation.
The mechanical processes are advection, dispersive
effects (hydrodynamic dispersion, channeling), and
diffusion. Radioactive compounds can also decay. As
a result of sorption processes, some solutes will move
more slowly than the ground water that is transporting
them; this effect is called retardation. Biological
transformation, radioactive decay, and precipitation
will decrease the concentration of the solute in the
plume but may not necessarily slow the rate of plume
movement. The following are the primary processes
that affect the mobility and concentrations of
radionuclides being transported by ground water:
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! Advection
! Dispersion
! Matrix Diffusion
! Retardation
! Radioactive Decay
Advection
The process by which solutes are transported by the
bulk movement of water is known as advection. The
amount of solute that is being transported is a function
of its concentration in the ground water and the
quantity of the ground water flowing.
Computer codes that account only for advective
transport and ignore dispersion and diffusionprocesses
generally take one of two approaches. The first
approach uses a semi-analytical method (Appendix C)
to solve the ground-water flow and transport equations,
whereas the second approach uses fully numerical
methods to determine the ground-water velocity field
from which directions and rates of solute movement
are calculated by the code.
The semi-analytical method frequently fails when
aquifers are of complicated shape and nonhomogen-
eous. In these instances, it is better to use the second
option which utilizes a fully numerical code for deter-
mining the velocity distributions and particle (i.e.,
solute) paths. This may be accomplished with either
finite-differences or finite-elements (Appendix C).
Computer codes that consider only advection are ideal
for designing remedial systems (e.g., pump and treat)
because the model output is in the form of solute
pathlines (i.e., particle tracks) which delineate the
actual paths that a contaminant would follow.
Therefore, capture zones created by pumping wells are
based solely on hydraulic gradients and are not subject
to typical problems that occur when solving
contaminant transport equations which include
dispersion and diffusion in the aquifer. These
problems are numerical dispersion and artificial
oscillation. Numerical dispersion arises because
computers have a limited accuracy, thus some round-
off error will occur in the computations. This error
results in the artificial spreading of contaminants due
to the amplification of the dispersivity. Hence, the
contaminant will disperse farther than it should with a
given physical, or "real" dispersivity. This extra
dispersion will result in lower peak concentrations and
more spreading of the contaminant. Methods exist to
control numerical dispersion, but the methods
themselves may introduce artificial oscillation.
Artificial oscillation is the over- or under-shooting of
the true solution by the model and results in inaccurate
solutions and may give erroneously high and low
concentrations.
There are other ground-water solute modeling situa-
tions where the phenomenon of dispersion, together
with its many uncertainties, is only a minor factor in
describing the transport of radionuclides in ground
water and can be ignored. For example, the flux of
contaminants entering a river that is recharged from a
contaminated aquifer is much less sensitive to
dispersion than the concentration in a particular well.
In the former case, the contaminated ground water
would enter over a wide area, which would tend to
smear out the effects of dispersion. For similar reasons,
the transport from nonpoint sources of con-tamination,
such as mill tailings and large landfills, would diminish
the sensitivity of the modeled results to dispersion. In
these instances, computer codes that consider only
advection may be appropriate.
As mentioned previously, advective codes are also
excellent in the remedial design stage for determining
the number and placement of extraction or injection
wells and in evaluating the effect that low permeability
barriers may have on the flow system. However, there
are a number of drawbacks that must be carefully
considered when selecting a code that ignores
dispersion and diffusion. The most significant of these
is that matrix diffusion, which is discussed below, can
be one of the most important processes that will
determine the length of time that a pump and treat
system must operate before clean-up goals will be met.
Without the ability to evaluate the effects of diffusion on
solute transport, it would be very difficult to estimate
remediation times accurately.
A second potential problem with advection-based codes
is that dispersion will tend to spread contaminants over
a much wider area than would be predicted if only
advective processes are considered, thereby
underestimating the extent of contamination. However,
because dilution is under-accounted for, unrealistically
high peak concentrations are generally obtained, which
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may be appropriate if conservative estimates are
desired.
Advective codes also tend to yield more accurate
travel-time determinations of unretarded contaminants
because the solution techniques are inherently more
stable, and numerical oscillations, which artificially
advance the contaminant front, are minimized.
Another important advantage of advective codes is that
the output (i.e., particle tracks) is a very effective
means of ensuring that ground-water gradients, both
vertical and horizontal, are consistent with the
conceptual model.
Hydrodynamic Dispersion
In the previous discussion, advective processes of
transport in porous media were presented. In reality,
the transport of contaminants is also influenced by
dispersion and molecular diffusion, which is caused by
the tendency of the solute to spread out from the
path that it would be expected to follow if only
transported by advection (Figure 4-9). This spreading
of the contamination over an ever-increasing area is
called hydrodynamic dispersion and has two
components: mechanical dispersion and diffusion.
Hydrodynamic dispersion causes dilution of the solute
and occurs because of spatial variations
in ground-water flow velocities and mechanical mixing
during fluid advection. Molecular diffusion, the other
component of hydrodynamic dispersion, is due to the
thermal kinetic energy of solute particles and also
contributes to the dispersion process. Thus, if
hydrodynamic dispersion is factored into the solute
transport processes, ground-water contamination will
cover a much larger region than in the case of pure
advection, with a corresponding reduction in the
maximum and average concentrations of the
contaminant.
Because hydrodynamic dispersion is the sum of
mechanical dispersion and diffusion, it is possible to
divide the hydrodynamic dispersion term into the two
components and have two separate terms in the
equation. Under most conditions of ground-water flow,
diffusion is insignificant and is frequently neglected in
many of the contaminant transport codes. However,
this artificial exclusion of the diffusion term may create
problems in certain instances as will be discussed under
the topic of matrix diffusion.
There is concern as to how adequately dispersion can be
represented in computer codes because it is related to
spatial scale and variations in aquifer properties which
are generally not explicitly simulated in the code (e.g.,
tortuosity). Furthermore, dispersion coefficients are
very difficult to measure in the field
DrS
Figure 4-9. Hydrodynamic Dispersion
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and are usually obtained during the model calibration
process.
These limitations suggest that not too much confidence
be placed in dispersion values, and that it is generally
best to use advection-dispersion-based codes to bound
the maximum probable extent that contamination may
have spread. However, as mentioned previously, peak
concentrations will tend to be underestimated.
Matrix Diffusion
Diffusion in solutions is the process whereby ionic or
molecular constituents move under the influence of
their kinetic activity in the direction of their
concentration gradient (Figure 4-10). The diffusion of
radionuclides from water moving within fractures, or
coarse-grained material, into the rock matrix or finer-
grained clays can be an important means of slowing
the transport of the dissolved radionuclides,
particularly for non-sorbing or low-sorbing soluble
species. The apparent diffusion coefficient for a given
radionuclide depends on properties that are intrinsic to
the chemical species (e.g., mobility) as well as
properties of the rocks (such as porosity, tortuosity, and
sorption ratios).
As stated previously, matrix diffusion is frequently
insignificant and is often neglected in many of the
contaminant-transport codes. However, potential
problems arise when matrix diffusion is ignored and
contaminant distributions are based solely on
advective-dispersive principles. For example, ground-
water pump and treat remediation systems work on the
premise that a capture zone is created by the pumping
well and all of the contaminants within the capture
zone will eventually flow to the well. The rate at which
the contaminants flow to the well may, however, be
very dependent on the degree to which the
contaminants have diffused into the fine-grained
matrix (e.g., clays). This is because the rate at which
they will diffuse back out of the fine-grained materials
maybe strongly controlled by concentration gradients,
rather than the hydraulic gradient created by the
pumping well. Therefore, matrix diffusion can
significantly retard the movement of contaminants,
and, if the computer code does not explicitly account
for this process, the overall effectiveness of the
remediation system (i.e., clean-up times) could be
grossly underestimated.
Other instances where matrix diffusion processes can
lead to erroneous model predictions is in the
determination of travel times, peak concentrations, and
flushing volumes. The fact that diffusion can play a
significant role in slowing the transport of
radionuclides suggests that, if it is ignored, travel
rates, as well as peak concentrations, will be
overestimated. Frequently, clean-up times are
estimated based on the flushing of a certain number of
pore volumes. However, matrix diffusion
in-',
j<>O.
Figure 4-10. Matrix Dispersion
4-39
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processes, if unaccounted for, can cause the number
of required pore volumes to be greatly underestimated.
This is because pore volume calculations generally
assume that water moves freely through all of the pores
and does not account for the relatively stagnant
conditions of fine-grained rocks in which contaminants
may have diffused.
Retardation
In addition to the physical processes, the transport of
radionuclides is affected by chemical processes. The
following summary of geochemical processes that
could potentially play a role in the transport of
radionuclides has been provided in order to offer an
appreciation of their wide variety and complexity:
! Sorption ~ the attachment of chemical
species on mineral surfaces, such as ion
exchange, chemisorption, van der Waals
attraction, etc., or ion exchange within the
crystal structure.
! Ion exchange phenomena ~ that type of
sorption restricted to interactions between
ionic contaminants and geologic materials
with charged surfaces which can retard the
migration of radionuclides.
! Speciation ~ the distribution of a given
constituent among its possible chemical forms
of the radionuclide which can influence its
solubility and therefore its rate of transport by
limiting the maximum concentration of the
element dissolved in the aqueous phase.
! Precipitation ~ the process by which
dissolved species exceed solubility limits,
resulting in a portion precipitating out of
solution.
! Natural colloidal formation ~ the attachment
of radionuclides to colloids resulting in a
mode of radionuclide transport or retardation
which involves the movement or mechanical
retardation of radionuclides attached to large
colloidal paniculate matter suspended in the
ground water or the formation of colloidal
clusters of radionuclide molecules.
! Radiolysis ~ the change in speciation due to
radiation or recoil during radioactive decay,
which can affect the solubility of
radionuclides.
! Biofixation ~ the binding of radionuclides to
the soil/organic matrix due to the action of
some types of microorganisms and plants,
thus affecting mobility of the radionuclide.
! Natural organic matter interactions ~ soil
organic matter can play a significant role in
mobilizing, transporting, sorbing, and
concentrating certain radionuclides.
! Anion exclusion ~ negatively charged rock
surfaces can affect the movement of anions,
by either retarding the movement of anions
by not allowing negatively charged
radionuclides to pass through the pore
opening, or by enhancing the transport of
ions by restricting the anion movement to the
center of the pore channel where ground-
water velocities are higher.
Obviously, a wide range of complex geochemical
reactions can affect the transport of radionuclides.
Many of these reactions are poorly understood and are
primarily research topics. From a practical view, the
important aspect is the removal of solute from solution,
irrespective of the process. For this reason, most
computer codes simply lump all of the cumulative
effects of the geochemical processes into a single term
(i.e., distribution coefficient) which describes the
degree to which the radionuclide is retarded relative to
the ground water. Thus, the distribution coefficient
relates the radionuclide concentration in solution to
concentrations adsorbed to the soil. Because the
distribution coefficient is strongly affected by site-
specific conditions, it is frequently obtained from batch
or column studies in which aliquots of the solute, in
varying concentrations, are well mixed with
representative solid from the site, and the amount of
solute removed is determined.
If the sorptive process is rapid compared with the flow
velocity, the solute will reach an equilibrium condition
with the sorbed phase, and there is a greater likelihood
that the distribution coefficient approach will yield
reasonable values. However, if the sorptive process is
slow compared with the rate of fluid flow, the solute
may not come to equilibrium with the sorbed phase
and geochemical (i.e., based on thermodynamics and
kinetics) models are generally required.
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Most computer codes assume that the distribution
coefficient is constant over all solute concentration
ranges (i.e., linear isotherm). However, this
assumption may place a serious limitation on the
predictive capability of the code, in that a linear
relationship between the concentration of solute in
solution and the mass of solute sorbed on the solid does
not limit the amount of solute that can be sorbed onto
the solid. In actuality, this is not the case; there must
be an upper limit to the mass of solute that can be
sorbed, due to a finite number of sorption sites on the
solid matrix. This upper bound on sorption suggests
that, in a natural system, retardation would decrease as
contaminant concentrations in the ground-water
increase. This discrepancy between computer codes
assuming linear sorption behavior when, in fact, non-
linear sorption is more accurate, can have important
implications when predicting the migration of the
center of mass versus the leading edge of a
contaminant plume, or when predicting required
pumping times for a pump and treat remedial action.
At high concentrations, the linear assumption will
over-predict retardation and under-predict radionuclide
travel rates and contaminant concentrations.
A basic assumption in code development is that at
dilute concentrations the errors associated with using
linear sorption isotherms to predict non-linear
relationships will be minimal. However, radionuclides
present a special problem in that frequently the
releases may be at dilute concentrations but over
extended durations. These long time frames may allow
all of the sorption sites to be filled, even at low release
concentrations, and model results will diverge from
actual values by under-predicting radionuclide travel
rates and concentrations.
The ability of a code to accommodate retardation
effects is essential for evaluating radionuclide transport
rates unless a special case is being considered, such as
one involving tritium which moves unretarded or if the
primary objective is to determine the absolute
minimum travel times and maximum travel distances.
It is possible to back out travel rates and distances from
computer codes that do not accommodate distribution
coefficients; however, if the species are decaying, the
calculations can become very tedious.
Radioactive Decay
Radionuclides decay to stable products or to other
radioactive species called daughters. For some
radionuclides, several daughter products may be
produced before the parent species decays to a stable
element. For some radionuclides, the daughter(s) may
present a potentially greater health risk than the
parent. Accounting for the chain-decay process is
particularly important for predicting the potential
impacts of uranium, thorium, and transuranic
migration.
In considering this process over the transport path of
radionuclides, one transport equation must be written
for each original species and each daughter product to
yield the concentration of each radionuclide (original
species and daughter products) at points of interest
along the flow path in order to estimate total
radiological exposures. However, not all computer
codes that simulate radioactive decay allow for
ingrowth of the daughters, which may not cause a
problem if the daughter half-lives are very long (i.e.,
they take a very long time to grow in) or if the
daughter products are of little interest. In addition, it
is computationally difficult to account for ingrowth of
daughters during transport. Codes that do address
daughter ingrowth generally account for ingrowth in
the contaminated zone only. The difficulty arises in
the need to use the Kd of the daughter and changes in
the travel distance as the daughters grow during
transport through the unsaturated and saturated zones.
4.3.1.4 Multiphase Fluid Conditions
The movement of contaminants that are immiscible in
water (i.e., non-aqueous phase liquids - NAPL)
through the vadose zone and below the water table
results in systems which have multiple phases (i.e., air,
water, NAPL). This coexistence of multiple phases
can be an important facet in many contaminant-
transport analyses. However, only the water and the
vapor phase are of concern when evaluating the
transport of radionuclides. A limited number of
radionuclides can form volatile species that are capable
of being transported in a moving vapor or gas. Among
these are tritium, carbon-14, and iodine-129. Over a
large scale, factors that affect transport in flowing
ground water also affect transport in flow-ing gas (i.e.,
the velocity of the gas determines the potential for
advective transport). In the absence of flow, diffusion
is the only mechanism for transport in the gaseous
state. The processes of partitioning of the volatile
species between the gaseous, liquid, and solid state and
isotopic exchange must also be consi-dered when
assessing the impact of vapor transport.
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Currently a number of analytical and numerical codes
allow the investigation of vapor transport in the
unsaturated zone; however, almost all of these codes
assume an immobile water phase. The limitation of
this assumption is that one of the principal concerns
regarding gaseous transport is its role in transporting
gas-phase radionuclides through the unsaturated zone
to the water table where they may be dissolved and
transported by the ground water. Without the
capability to simulate the percolation of water through
the unsaturated zone, tritium concentrations reaching
the water table will be greatly underestimated.
Furthermore, remediation strategies cannot be fully
developed if the residual water held in the unsaturated
zone is assumed to remain stagnant. For instance, a
method that has been proposed to remediate tritium
involves pumping the tritiated water from withdrawal
wells located downgradient from the source area. The
contaminated water is subsequently reinjected into
wells upgradient from the withdrawal wells. In this
manner, tritium is recycled continuously until it decays
to levels below the remedial criteria (e.g., the drinking
water standards). Two aspects of this system that
could not be evaluated without having the ability to
simulate mobile water and vapor in the unsaturated
zone are, first, whether vapor transport will carry
tritium beyond the limits of the hydraulic capture zone
created by the pumping wells, and second, what the
expected loading rates will be from the source term.
4.3.1.5 Flow Conditions
The ground-water environment can be divided into a
variably saturated (vadose zone) and saturated regimes.
The irregular surface that forms the boundary between
these two regimes is known as the water table. Below
the water table, pressures are equal to or greater than
atmospheric and the pores and spaces within and
between individual soil particles are filled with water.
Above the water table, in the partially saturated zone,
water is generally under negative pressure or tension
(less than atmospheric). Some of the pore space is
usually occupied by gases derived primarily from the
atmosphere as well as pore water.
Radionuclide releases to the ground water may result
from a number of mechanisms. These mechanisms
can affect ground water directly or indirectly, and they
include the following:
! Direct discharge (e.g., on-site release from
treatment processes)
! Leachate generation (e.g., from buried
wastes, surface impoundments, and
absorption beds)
! Overland flow (e.g., from impoundment
overflow or failure, drum leakage)
! Contaminated stream interaction with
aquifers
The decision as to whether the vadose zone and/or
saturated zone will be modeled is directly related to the
mechanism by which the contamination was released.
That is, if radionuclides are being released directly to
the water table, little would probably be gained by
modeling the vadose zone. However, if the risk
assessment is based only on radionuclide
concentrations reaching the water table, it may not be
necessary to model the saturated zone.
After a determination is made as to whether the vadose
zone and/or saturated zone are to be modeled, it
becomes necessary to address a much more difficult
question, i.e., the complexity at which each zone
should be modeled. This question can be answered
only by attaining a thorough understanding of the
modeling objectives, as well as an appreciation of the
advantages and disadvantages of each prospective
approach.
The sophistication of the unsaturated zone modeling
approach will be based primarily on the overall
modeling objectives, although the complexity of the
hydrogeology may also play a significant role. For
instance, accurate predictions of radionuclide flow and
transport through a very complex unsaturated zone
may be irrelevant and unnecessary if credit is not taken
for it in the baseline risk assessment. On the other
hand, if the risk assessment is based solely upon
arrival times and peak concentrations of radionuclides
arriving at the ground-water table, then a detailed
analysis of flow and transport through even a thin,
uncomplicated unsaturated zone may be significant
and require complex modeling.
Relative to saturated zone modeling, vadose zone
modeling is characterized (plagued) by significant
numerical difficulties and greater uncertainty
regarding conceptualization and parameter estimation.
In many vadose zone modeling situations, it may be
advisable to use simple models and conservative
assumptions to estimate exposure concentrations. The
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appropriate level of modeling and data collection for
risk assessment at individual sites should be
determined during the remedial process.
Situations may arise where reliable simulations of flow
and transport of radionuclides through the unsaturated
zone may not be possible even with complex ground-
water models. In particular, if the unsaturated zone is
indurated with fractures or macropores with high
permeability, the flow and transport processes become
so involved that mathematical formulations of porous
media transport are poor representations of the
physical phenomena. Furthermore, localized zones of
higher permeability may cause the wetting front to
advance at highly variable rates, which may introduce
significant disparities between the actual and predicted
contaminant concentrations.
Under single-phase flow conditions, an option to select
a vadose zone code which simulates hysteresis is
provided. Hysteresis is simply a term which describes
the fact that wetting and drying curves for a certain
soil (pressure head versus volumetric water content),
under partially saturated conditions, are not the same.
That is, the pressure head is not only dependent upon
the water content but also on whether water is being
removed or added to the system. The effect is due to
both the geometric shapes of the pores and the contact
angle between the water and the mineral surface,
which is different depending on whether the water is
advancing and retreating. Of particular relevance in
considering hysteric effects as a code-selection criteria
is that hysteresis will have little effect on the flow and
transport of contaminants. The primary utility of
including hysteresis is to account for this process
during model validations studies. Therefore, if model
validation will not be performed, which will be the
case in the vast majority of modeling studies, the
capability of a code to simulate hysteresis will be of
little importance.
4.3.1.6 Time Dependence
The most frequently performed ground-water modeling
is that of the saturated zone. The parameter needs are
well defined and the field data collection activities are
relatively straightforward. The major factors that
provide immediate insight into whether sophisticated
ground-water modeling will be necessary are the
complexity of the:
! Source term
! Dominant flow and transport processes
1 Hydrogeology (e.g., layers, heterogeneity)
I
Hydraulic boundaries
Previous discussions have addressed the relative
importance of these issues in the code selection
process. However, one aspect that has not been fully
considered is the temporal nature of flow and transport
within the system. As discussed previously,
simulations can be performed in either a steady or a
transient state. At steady-state, it is assumed that the
flow field and contaminant releases remain constant
with time, whereas a transient system simply means
one that fluctuates with time. This fluctuation may be
induced by both natural (e.g., tides, rainfall) and
manmade influences (e.g., wells, hydraulic barriers).
In many instances, transient systems, if observed over
the long term, will approach relatively steady-state
conditions.
As far as code selection is concerned, relative to the
temporal behavior of the system, it is a fairly
straightforward decision. Namely, most analytical
models do not simulate a transient flow system;
therefore, if a transient flow system needs to be
modeled, analytical and semi-analytical methods are
generally not available. Furthermore, if a steady-state
flow system is acceptable, but a transient transport
capability is required, both analytical and numerical
codes are readily available for these conditions and the
selection criteria should be deferred to other
considerations.
4.3.2 Code-Related Characteristics
In addition to the site-related characteristics presented
in the previous section, the code selection process must
also consider attributes that are integral components of
the computer code(s), including:
! Geometry
! Source Code Availability
! Code Accessibility/Ease of Use
! Code Verification and Validation
! Code Output
! Solution Methodology (Appendix C)
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4.3.2.1 Geometry
The decision to model a site in a particular number of
dimensions should be based primarily upon both the
modeling objectives and the availability of field data.
Other considerations include whether a computer code
exists that can simulate the dominant processes in the
desired number of dimensions, and whether hardware
requirements are compatible with those available.
In determining how many dimensions are necessary to
meet the objectives, it becomes necessary to gain a
basic understanding of how ground-water flow and
contaminant concentrations are affected by the
exclusion or inclusion of an additional dimension. It
should be kept in mind that the movement of ground
water and contaminants is usually controlled by
advective and dispersive processes which are
inherently three-dimensional. Advection is more
responsible for the length of time (i.e., travel time) it
takes for a contaminant to travel from the source term
to a downgradient receptor, while dispersion directly
influences the concentration of the contaminant along
its travel path. This fact is very important in that it
provides an intuitive sense for what effect
dimensionality has on contaminant migration rates and
concentrations. As a general rule, the fewer the
dimensions, the more the model results will over-
predict concentrations and under- predict travel times.
Concentrations will be over- predicted because
dispersion, which is a three-dimensional process, will
be dimension limited and will not occur to the same
degree as it actually would in the field. Travel times
will be under-predicted, not because of a change in the
contaminant velocities, but because a more direct
travel path is assumed. Therefore, the lower
dimensionality models tend to be more conservative in
their predictions and are frequently used for screening
analyses.
One-dimensional simulations of contaminant transport
usually ignore dispersion altogether, and
contamination is assumed to migrate solely by
advection, which results in a highly conservative
approximation. Vertical analyses in one dimension are
generally reserved for evaluating flow and transport in
the unsaturated zone.
Two-dimensional analyses of an aquifer flow system
can be performed as either a planar representation,
where flow and transport are assumed to be horizontal
(i.e., longitudinal and transverse components), or as a
cross section where flow and transport components are
confined to vertical and horizontal components. In
most instances, two-dimensional analyses are
performed in an areal orientation, with the exception
of the unsaturated zone, and are based on the
assumption that most contaminants enter the saturated
system from above and that little vertical dispersion
occurs. However, two-dimensional planar simulations
have a number of limitations. These include the
inability to simulate multiple layers (e.g., aquifers and
aquitards) as well as any partial penetration effects.
That is, the contaminant source, wells, rivers, lagoons,
and lakes are all assumed to penetrate the entire
thickness of the aquifer. Furthermore, because vertical
components of flow are ignored, a potentially artificial
lower boundary on contaminant migration has been
automatically assumed which may or may not be the
case.
A two-dimensional formulation of the flow system is
frequently sufficient for the purposes of risk
assessment, provided that flow and transport in the
contaminated aquifer are essentially horizontal. The
added complexities of a site-wide, three-dimensional
flow and transport simulation are often believed to
outweigh the expected improvement in the evaluation
of risk. Complexities include limited site-wide
hydraulic head and lithologic data with depth and
significantly increased computational demands.
Quasi-three-dimensional analyses remove some of the
limitations that are inherent within two-dimensional
analyses. Most notably, quasi-three-dimensional
simulations allow for the incorporation of multiple
layers; however, flow and transport in the aquifers are
still restrained to longitudinal and transverse
horizontal components, whereas flow and transport in
the aquitards are even further restricted to vertical flow
components only. Although partial penetration effects
still cannot be accommodated in quasi-three-
dimensional analyses, this method can sometimes
provide a good compromise between the relatively
simplistic two-dimensional analysis and the complex,
fully three-dimensional analysis. This is the case,
particularly if movement of contaminants from the
shallow aquifer through a confining unit and into a
deeper aquifer is suspected.
Fully three-dimensional modeling generally allows
both the geology and all of the dominant flow and
transport processes to be described in three
dimensions. This approach usually affords the most
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reliable means of predicting ground-water flow and
contaminant transport characteristics, provided that
sufficient representative data are available for the site.
Fully three-dimensional analyses are often the only
defensible means to evaluate the effectiveness of many
potential remedial scenarios. For example, extraction
and injection wells may create strong vertical
gradients, as well as three-dimensional capture zones.
Without the ability to accommodate these gradients
and capture zones, dilution effects and capture zones
could be over- or underestimated. The ground-water
flow and contaminant transport beneath a barrier wall
would also be subject to serious predictive limitations
without a three-dimensional analysis, againbecause of
the strong vertical gradients that generally accompany
these features.
4.3.2.2 Source Code Availability
As a general rule, an effort should be made to use
publicly available computer codes, provided they have
been well documented and tested and can meet all of
the major requirements of the modeling objectives. In
certain instances, however, it may be necessary to
purchase a proprietary code. A proprietary code may
be needed for a number of reasons, but, most
commonly, proprietary codes are selected either
because the user is familiar with the code or because
the publicly available codes would not meet the
modeling objectives.
The following is a list of factors that need to be
considered during the selection process of both
proprietary and non-proprietary computer codes:
! Whether the code has been widely used and is
generally accepted by the technical
community;
! How well the code is documented and
verified;
! Whether the code has been independently
peer reviewed;
! Whether the purchase price of the code
provides any technical support, and, if
additional support is required, what it will
cost;
! Whether the source code is provided, and, if
not, under what conditions could it be
obtained if necessary;
! Whether the code has ever been applied to a
similar problem with consistent objectives;
! Whether the code has been field tested on
problems directly relevant to the subject site;
! Whether the code has ever been used to
support a case in litigation or regulatory
enforcement action;
! Whether any additional enhancements or
modifications to the code are planned in the
future.
4.3.2.3 Code Testing and Processing
The verification process is generally undertaken during
the developmental stages of the computer code. It is a
procedure in which analytical equations of known
solutions are used to ensure that there is an agreement
between the formulations and solutions of the same
basic equations, which are solved with more complex
numerical methods. In some instances, numerical
methods, which have been verified with analytical
solutions, are used to check other newly formulated or
even more complex numerical solutions. The purpose
of verification is to show only that the numerical
techniques work and that no errors exist in either the
mathematical formulation or in the actual coding of
the formulation.
One important aspect of code verification is that it can
usually be performed independently of the code
development process. This allows the accuracy of
codes to be checked even without access to the source-
code documentation. It is not recommended, however,
that codes be selected that were not verified during the
development process and are not well documented.
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Calibration and validation are activities designed to
test the realism of the ground-water flow and transport
model. From a philosophical perspective, calibration
and validation are very different. When addressing the
subject of calibration, it is generally assumed that both
the conceptual model and numerical models are
reasonably correct or adequate. Therefore, to calibrate
a model, model parameters are simply adjusted within
an acceptable range, based on site-specific
measurements, to arrive at a best fit of the dependent
variable, which is usually hydraulic head or solute
concentrations. Validation, on the other hand,
examines in more detail the realism of both the
conceptual model and the numerical model.
Model calibration of vadose zone models is very
difficult and rarely attempted primarily due to data
limitations, whereas calibration of saturated flow and
transport models is relatively straightforward, provided
there are sufficient field measurements of hydraulic
head or solute-concentration data. One potential
problem with calibration of saturated flow models is
that a unique solution for the hydraulic head
distribution is not available if all of the boundary
conditions are either no-flow or fixed head. In other
words, if the model does not contain a flux condition
of significant magnitude (relative to total flux through
the model), increasing or decreasing all the hydraulic
conductivities in equal proportion will result in the
exact same hydraulic head distribution. The only
difference is that the amount of flux through the model
will be increased or decreased in proportion to the
change in hydraulic conductivities. This is why it
becomes very important to not only narrow the
probable ranges of hydraulic conductivities through
methods such as aquifer tests but also to use mass
balance information to check the calibration results.
Model validation is, in general, a comparison of the
solutions of the mathematical equations from which
the model is formulated with field-measured data.
Compelling arguments have been made that ground-
water models cannot be validated, only invalidated
(KON92). Accordingly, validation is best thought of
as a process for determining the degree to which a
model can be relied upon to support a specific
modeling objective at a specific site. Validation, at
best, may consist of reasonable agreement between
simulated results and actual field data at two or more
time periods.
Attempts to validate models must address the issue of
spatial variability when comparing model predictions
with limited field observations. If sufficient field data
are obtained to derive the probability distribution of
contaminant concentrations, the results of a stochastic
model can be compared directly. For a deterministic
model, however, the traditional approach has been to
vary the input data within its expected range of
variability (or uncertainty) and determine whether the
model results fall within the bounds of field-measured
values.
Regardless of whether the solution is obtained by
analytical or numerical techniques, true validation or
history matching canbe done only through comparison
with field measurements and, in some cases, laboratory
data. Furthermore, given the lack of comprehensive
field data sets that adequately describe the spatial
parameter distributions, and our inability to directly
measure water and solute fluxes which are more
logical variables for model validation, it is highly
unlikely that complete validation of any simulation
model canbe possible.
Such complete validation, however, is not necessary
for most modeling approaches if model limitations are
adequately recognized. It should also be kept in mind
that validation is site-specific and consequently its
utility, if achieved at one location, is limited when
considering application of the model at another
location.
The need for the overall validation or history matching
outlined above is directed at the creation of reasonably
reliable computational and forecast capabilities for
studies that would generally go beyond the baseline-
risk assessment. It is acknowledged that the field
testing efforts outlined here usually occur concurrently
with the remedial process; however, validation or field
testing is not simply applying models within the
remedial investigation context. This is because the
remedial investigation of a waste site may strongly
focus on the calculation of risk. For example, if all
contaminants released at a waste site are immobile, the
remedial investigation activities in support of the
baseline risk assessment may concentrate on the
quantification of partitioning between the water and
the solid phase. As such, simplified flow and transport
models may be used to support the baseline risk
assessment under this situation. Within this context,
it is recognized that flow and transport modeling is
only one component of the risk calculation, and those
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responsible for the quantification of the baseline risk
assessment may employ a relatively unsophisticated
modeling approach for the baseline and perhaps very
conservative simulations. On the other hand, for other
situations, detailed flow and transport analyses may be
required. Under these conditions, resolution of the
flow and transport model validation issue will require
examination of the waste site with models of some
complexity or sophistication with regard to the
geologic structure and dominant processes.
4.3.2.4 Model Output
One aspect of the computer code that is frequently
ignored in the selection process is the form that the
model output will take. It is true, however, that in
most instances the actual output can be fashioned into
the desired format, provided the model itself is
consistent with required output. That is, output in
three dimensions cannot be obtained with a two-
dimensional model.
In general, the model output is expressed in terms of
hydraulic head, pressure, or solute concentrations. The
spatial coverage of parameter output values is either
dependent on the frequency of nodal spacing
(numerical) or on the number of specified x and y
coordinates (analytical) which are included in the
model input files. Code output will also vary due to
the inherent nature of the code itself. For example,
codes that simulate movement in the unsaturated zone
produce what are termed saturation profiles. These
profiles indicate what percentage of the pore space is
filled with water, whereas saturated zone codes have
no need for this capability because all of the pores
below the water table are assumed to be filled.
Some codes provide output in a format which is very
useful and saves time during the post-processing of the
data. The best example of this is where the user can
specify nodes where concentration profiles are desired
with time (i.e., breakthrough curves). These profiles
allow arrival times, peak concentrations, and
contaminant mass changes to be easily evaluated.
The single most important code selection criteria,
relative to the model output, would be that the code
provides mass-balance information. A mass-balance
determination is a check to ensure that at steady-state,
the amount of water or contaminant mass entering the
system equals the amount exiting the system. If inflow
does not equal outflow for a steady-state simulation,
there may be something wrong with the numerical
solution, although errors in the mass balance may also
indicate that there are problems with the mass balance
formulation itself. Therefore, mass-balance
information not only provides a check on the
mathematical formulations within the code, but it also
assists in ensuring that input parameter conversions
and other errors have not been made.
It is not uncommon for codes that do include mass-
balance output to provide information (e.g., fluxes,
heads) on specific boundaries as well as the source
term, all of which can be used in the interpretation and
evaluation of the predicted flow and solute transport
directions and rates.
4.4 MODELING DILEMMAS
The previous sections have described how site- and
code-related features affect the model selection
process. What is not presented, however, is a
discussion of the processes that are very difficult, if not
impossible, to model with currently available models.
Complex flow and transport processes present another
difficulty in that computer codes currently do not exist
that explicitly accommodate a number of these
processes including:
! Turbulent Ground-Water Flow
! Facilitative Transport
! Unsaturated Fracture Flow
! Complex Geochemical Reactions
Although these processes are very complex, it is
important that at least a basic understanding of these
mechanisms and concepts be grasped prior to initiating
field or modeling investigations in which they may be
important. The subsequent discussion will introduce
the difficulties associated withmodeling these complex
processes. Of particular relevance is that the processes
are not fully understood and are, therefore, not well
described mathematically. If modeling is not possible
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because of the overall complexity of the site
characteristics, it is common for a greater emphasis to
be placed on empirical rather than predicted data.
This may involve establishing long-term monitoring
programs, which in effect, have objectives similar to
those of ground-water modeling.
Turbulent Ground-Water Flow. As ground-water
velocities increase, flow diverges from the laminar-
type which is characteristic of low velocities and
becomes more turbulent. At the point in which
turbulent flow is reached, a basic law describing the
relationship between hydraulic gradient and specific
discharge (i.e., Darcy's) breaks down and is no longer
valid. Most ground-water flow, however, is not
turbulent, except in the very close proximity of large
pumping or recharging wells. In practice, however,
turbulent flow over relatively small areas is generally
ignored without introducing any severe limitations in
the modeling. On the other hand, in cases where
turbulent flow is observed over relatively large areas,
such as cavernous limestone aquifers, Darcy's law may
be significantly violated and results from flow and
transport modeling would be of questionable value.
Facilitative Transport of Radionuclides. Field and
laboratory investigations have indicated that under
certain conditions contaminants are more mobile than
would be predicted based on properties such as
solubility, ion exchange, speciation, sorption-
desorption and ground-water velocities. These
predictions, however, have not accounted for the
potential interactions between the inorganic
contaminants and mobile colloids. Colloidal-size
particles include humic substances, clay minerals, iron
oxides and microorganisms. Colloids not only have a
high surface area per unit mass and volume, but many
types of colloids are also extremely reactive sorbants
forradionuclides. Therefore, radionuclides that might
otherwise be sorbed to stationary material in the
aquifer could be transported in the sorbed layers of
these mobile colloids. Sorption in this case has
facilitated transport.
A number of actinides, plutonium in particular, can
form natural colloids under conditions of near-neutral
solutions of low ionic strength. It is also suspected that
americium may form colloids under similar conditions.
Colloidal particles (up to 0.5 micrometers in diameter)
remain suspended for long periods and hence may
migrate with the ground water. As the solid waste
form is leached, particles containing radionuclides may
form by the sorption of dissolved radionuclides on
nonradioactive particles. At this time it is believed
that plutonium and americium are most likely to be
transported as colloids, although other radionuclides
might be subject to this transport process under certain
conditions. Transport of particulates in geologic
media will depend on aqueous flow rate, on pore and
fracture size in the rock, on ions carried in the water,
and on the nature of the paniculate matter. Several
mechanisms may remove colloidal particulates from
ground water such as mechanical filtration by the rock
matrix, sorption on the surface of the rock pores (van
der Waals), and neutralization of the repulsive charges
on the colloids, thus allowing them to coagulate.
Radiocolloids may arise from a variety of sources. The
corrosion of metal containers can lead to the formation
of absorbent colloids. Degradation of engineered
backfills may also lead to colloidal formation. If the
waste form is leached by ground water, naturally
occurring colloids derived from smectites,
vermiculites, illites, kaolinite, and chlorite present in
ground water may also adsorb radionuclides.
The degree to which facilitative transport can be
modeled is largely dependent upon the objectives of the
modeling and the extent of understanding of the
transport mechanisms active at the site. A site-specific
evaluation may be required to determine the possible
importance of colloidal transport on the mobility of the
radionuclides. To estimate the amount of
radionuclides that could be transported by colloidal
suspension, it is first necessary to determine whether
colloidal-sized particles exist in the ground water.
Then, the sorption ratios for waste elements on these
particles must be measured or estimated from the
composition of the particles. In addition, the
conditions under which colloids could form from the
waste elements or from the waste and their stability
after formation must be determined. Finally, the
conditions necessary for the filtration or sorption of the
particles by the rock matrix itself must be defined.
An alternative approach to detailed site investigations
to characterize the potential for colloidal transport
would be to undertake a conservative approach and set
all of the distribution coefficients to zero. This
approach, however, may not always be conservative in
that it is possible that under certain circumstances
colloids may have a velocity greater than the average
linear ground-water velocity. This may be due to both
size-exclusion and charge-repulsion. Size-exclusion
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occurs when molecules or ions are so large that they
cannot be transported through the smaller pores. As a
result, they are restricted to the larger pores, in which
the ground-water velocity is greater than average. The
charge-repulsion phenomenon occurs when the
colloids have a negatively charged surface which is
repelled by the negatively charged clays which line the
pore channels. This process may confine the colloid to
the central part of the channel where the velocities are
highest and the ground-water velocity is greater than
average.
Attempts have also been made to model the transport
of colloids which are more mobile than water by
setting the distribution coefficient to less than zero.
This approach, however, has a number of problems.
One of the most significant of these is that all of the
waste released from the source term would be assumed
to be transported as colloids which may result in overly
conservative solutions.
Currently, ground-water models do not exist that
describe the constitutive relationships involved with
colloidal transport and explicitly account for the
dominant geochemical interactions responsible for
colloidal transport.
Unsaturated Fracture Flow. As previously discussed,
ground-water modeling of the unsaturated zone is
based upon developing sets of moisture-characteristic
curves, that is the functional dependence of liquid-
water saturation and relative hydraulic conductivity on
the liquid-water potential within the rock matrix and
fractures for each hydrogeologic unit. In unfractured
rocks, these relations refer to the storage and
movement of liquid water within and through the
interstitial pore space. In fractured rocks, allowance
must be made for the storage and movement of water
within the interconnected fracture openings as well as
for the movement of water between the fracture
openings and the rock-matrix pore space. Standard
field and laboratory methods are not yet available by
which to determine the moisture-characteristic
relations for fractures within the unsaturated zone.
Liquid-water storage within fractures probably is
insignificant, but the flow of liquid water within and
across fractures is not yet well understood. Theoretical
models for liquid-water flow in single unsaturated
fractures have been developed but have not yet been
field tested. Fractures may or may not impede liquid-
water flow at low matrix saturations, and longitudinal
flow within the fractures may dominate liquid-water
flow above some critical matrix saturation.
Consequently, at high matrix saturations, fracture
systems and fault zones may become highly efficient
pathways for liquid-water flow. Liquid-water flow
within fractures may or may not be Darcian (i.e.,
laminar) and will be dependent on the gradient and
hydraulic conductivity.
At low matrix saturations, little or no water moves
longitudinally within the fracture openings, and the
effective hydraulic conductivity is controlled by that of
the fracture-bounded matrix blocks. As the matrix
approaches complete saturation, however, the
movement of water within and along the fracture
aperture rapidly becomes more efficient so that at
complete saturation the fractures may be dominant
contributors to the net hydraulic conductivity. The
relative contributions of fractures and matrix to the net
effective hydraulic conductivity depend on the fracture
frequency, aperture-size distribution, and degree of
interconnectivity. However, there is currently no way
to generate a complete set of fracture location and
geometry data.
In essence, a generally poor understanding of the
physics controlling fluid flow in fractured-unsaturated
systems, in conjunction with an inability to
characterize the fracture properties and locations,
makes it nearly impossible to model these systems
reliably.
Complex Geochemical Reactions. Radionuclides are
undergoing geochemical reactions. The principal
geochemical properties and processes of the
radionuclides, which may be site-specific and
important to understand, include the following:
! Complexation
! Phase transformations
! Adsorption and desorption
! Precipitation
As stated previously, if it is desired to model these
processes explicitly, as opposed to using simplifying
assumptions such as default or aggregate retardation
coefficients, geochemical rather than flow and
transport models may be required. As indicated, some
of the more common radionuclides, such as uranium
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and plutonium, can exist in a number of chemical
states, which can significantly affect their rate of
transport. Other radionuclides, such as tritium, are
relatively insensitive to the site geochemical conditions
but undergo phase transformations which are difficult
to simulate with existing codes. Explicit geochemical
models can be applied to assist in evaluating the
general effect that the geochemical environment will
have on the radionuclide fate and transport, but even
these methods are often unreliable and the results must
be interpreted carefully.
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SECTION 5
THE CODE SELECTION PROCESS
Section 4 described the various waste and site characteristics and processes and the code-related characteristics
pertinent to the code selection process. The emphasis was placed on recognizing when specific waste, site, and code
characteristics are important and therefore must be considered in order to meet the modeling needs of each phase of
the remedial process. This section presents the basic procedure that should be followed in evaluating ground-water
flow and transport code(s) prior to making a final selection among two or more potential codes.
5.1 OVERVIEW OF THE CODE REVIEW AND
SELECTION PROCESS
Verification
Validation
Given that an investigator understands the various
waste and site characteristics that need to be modeled
in order to meet specific modeling objectives, there
will often be several suitable computer codes which
could potentially be chosen from a large number of
codes published in the scientific literature (BAC80,
EPA91, and MOS92). As mentioned in Section 1,
IMES "Integrated Model Evaluation System" provides
an excellent computerized means by which codes may
be screened automatically for their respective
capabilities. The user simply checks off the desired
code capabilities within a screening module of IMES,
and the program eliminates all of the codes without the
specified capabilities from an extensive internal
database. Furthermore, IMES will provide some
information on the code itself although these
descriptions are, in many instances, somewhat limited.
Ideally, a detailed evaluation of each candidate code
should be performed to identify the one most
appropriate for the particular site and modeling
objectives. The resources to complete a detailed study
are seldom available, and usually only one to two codes
are selected based upon a cursory review of code
capabilities. Regardless of whether a detailed or more
cursory review is performed, it is important for the
reviewer to be cognizant of the following factors and
how they will affect final code selection:
1. Code Capabilities Consistent with:
User needs
Modeling objectives
Site characteristics
Contaminant characteristics
Quality and quantity of data
2. Code Testing
Documentation
3. History of Use Acceptance
The first aspect of the review concentrates on the
appropriateness of the particular code to meet the
modeling needs of the project. This subject is
discussed in depth in Sections 3 and 4. The reviewer
must also determine whether the data requirements of
the code are consistent with the quantity and quality of
data available from the site. Next, the review must
determine whether the code has been properly tested
for its intended use. Finally, the code should have
some history of use on similar projects, be generally
accepted within the modeling community, and be
readily available to the public.
Evaluating a code in each of the three categories would
take a significant effort, especially with respect to code
testing. Theoretically, the reviewer should obtain a
copy of the computer code, learn to use the code, select
verification problem sets with known answers, and
compare the results of the model to the benchmark
problems. This task is complicated, largely because no
standard set of benchmark problems exists, and the
mathematical formulation for each process described
within the code has to be verified through the
benchmarking process. Primarily for this reason,
selection of codes that are already widely tested and
accepted is recommended. Code validation, which
involves checking the model predictions against actual
field investigations designed specifically to test the
accuracy of the model, would almost never be practical
during the code evaluation and selection process.
The selection and evaluation process presented in this
section takes an approach which is consistent with
industry standards by relying on published reports and
user interviews as a substitute for actual hands-on
testing. The result is a code selection and evaluation
5-1
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process that provides a reasonable technical review
that is relatively straightforward and takes a relatively
short time to complete (Figure 5-1).
The model evaluation process presented in subsequent
sections involves the following steps:
1. Contact the author or curator of the code and
obtain the following:
Documentation and other model-related
publications
List of users
Information related to code testing
2. Read all publications related to the model,
including documentation, technical papers,
and testing reports.
3. Contact code users to find out their opinions.
4. Complete the written evaluation using the
criteria shown in Table 5-1.
Much of the information needed for a thorough
evaluation can be obtained from the author or
distributor of the code. In fact, inability to obtain the
necessary publications can indicate that the code is
either not well documented or not widely used. In
either case, inaccessibility of the documentation and
related publications should be grounds for evaluating
the code as unacceptable.
Most of the items in Table 5-1 should be described in
the code documentation, although excessive use of
modeling jargon may make some items difficult to
find. For this reason, some assistance from an
experienced modeler may be required to complete the
evaluation. Detailed conversations with users can also
be used to decipher cryptic aspects of the
documentation.
The evaluation process recommended in the following
sections relies on user opinions and published
information to take the place of hands-on experience
and testing. User opinions are especially valuable in
determining whetherthe code functions as documented
or has significant errors (bugs). In some instances,
users have performed extensive testing and
benchmarking or are familiar with published papers
documenting the use of the code. In essence, the
proposed evaluation process substitutes second-hand
experience for first-hand knowledge (user opinions) to
shorten the time it takes to perform the review. It is
also important to keep in mind that code selection is a
very dynamic process, and multiple codes may need to
be selected over the remedial lifetime of the site in
order not only to reflect the remedial phase of the
project, but also to remain current with existing
technology.
Models attempt to simulate natural processes through
a series of mathematical expressions. Because of the
simplifications and assumptions needed to simulate
these processes, all models will be inexact and
imprecise. Thus, it is important to understand the
magnitude of these deficiencies prior to the selection
and/or application of any model. As a first step in this
process, available documentation on the model must be
reviewed and evaluated to determine if the documented
capabilities of the model correspond with the objectives
of the study. Code documentation is, however, often
biased and in many cases incomplete. Furthermore,
major inherent weaknesses of the code (e.g., omission
of a process such as daughter in-growth) may not be
highlighted. For this reason, it is important to secure
or prepare independent reviews of any code before it is
selected. These reviews can be obtained from the
literature and supplemented with code-specific
evaluations similar to those presented in this report.
To the extent possible, the code should be exercised
with representative data prior to its final selection.
Failure to conduct such audits and benchmark testing
may result in the inappropriate selection of a code and
in a waste of time and resources.
As the user friendliness of the codes increase, the
practical expertise of the user typically decreases. This
is a potentially dangerous situation because of the large
potential for code misuse. In prior years when codes
were available only in mainframe-type environments,
they were almost always used by "experts" who had
knowledge of the capabilities of a selected code. Based
on this knowledge, appropriate inputs would be used
in a modeling effort. Now,
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Project Manager
and
Technical Support Staff
Development of Relevant
Code Selection Criteria
Based on Site and Code Characteristics
(Sections 3 and 4)
Preliminary Screening of Potential Computer Codes
(e.g. IMES)
Evaluate Relative
Importance of
Criterion
Is
Criterion
Critically
Important?
Does Code Meet
Criterion?
Enter Attribute into
Code Capability Table
(Appendix D)
Preliminary Identification of
Potential Code(s) That
Meet Critical Criterion
Detailed Code Evaluation
and Final Selection
(Chapter 5)
Contact Author
Review Relevant
Publications
Contact
Code Users
Document Findings
FINAL CODE SELECTION
Figure 5-1. Code Selection Review Process
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Table 5-1. Model Selection Criteria
CRITERIA
Section 5.2.1 Administrative Data
Author(s)
Development Objective (research, general use, education)
Organization(s) Distributing the Code
Organization(s) Supporting the Code
Date of First Release
Current Version Number
References (e.g., documentation)
Hardware Requirements
Accessibility of Source Code
Cost
Installed User Base
Computer Language (e.g., FORTRAN)
Section 5.2.2 Remedial Process
Scoping
Characterization
Remediation
Section 5.2.3 Site-Related Criteria
Boundary/Source Characteristics
Source Characteristics
Multiple Sources
Geometry
line
point
area
Release type
constant
variable
Aquifer System Characteristics
confined aquifers
unconfined aquifers (water-table)
aquitards
multiple aquifers
convertible
Soil/Rock Characteristics
heterogeneity in properties
anisotropy in properties
fractured
macropores
layered soils
Transport and Fate Processes
dispersion
advection
diffusion
density dependent
partitioning between phases
solid-gas
solid-liquid
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Table 5-1. (Continued)
CRITERIA
equilibrium isotherm:
linear (simple retardation)
Langmuir
Freundlich
nonequilibrium isotherm
radioactive decay and chain decay
speciation
Multiphase Fluid Conditions
two-phase water/NAPL
two-phase water/air
three-phase water/NAPL/air
Flow conditions
fully saturated
variably saturated
Temporal discretization (steady-state or transient)
5.2.4 Code-Related Criteria
Source Code Availability
History of Use
Code Usability
Quality Assurance
code documentation
code testing
Hardware Requirements
Solution Methodology
Code Output
Code Dimensionality
default values are available, and it is possible for a user
with only limited knowledge to produce a result. This
result may, however, be highly inaccurate, and the user
may be unaware of potential errors.
5.2 EVALUATION CRITERIA
The code(s) to be used for a particular application will
satisfy a combination of needs defined by the
intersection of regulatory requirements, site
characteristics, and attributes of the code (Figure 5-2).
The code review process outlined within the next
sections is based upon a complete and consistent set of
evaluation criteria. The evaluation process follows a
scheme which groups evaluation criteria based on their
similarity to one another. That grouping is reflected
in the organization of Table 5-1. Yet the selection
process must also account for the interrelationships
between evaluation criteria. For example, certain
groups of criteria will influence model selection and
evaluation in different ways. Some criteria are
important in choosing among codes, others in
controlling the way the code operates, and still others
in how the results can be interpreted and applied. In
the discussion that follows, these criteria are described
in terms of the way in which they influence the code
selection process.
5.2.1
Administrative Data
Few administrative data are, in fact, discriminatory
criteria, yet some administrative data may be indicative
of factors that exert overwhelming control over the use
of codes. Thus, codes must be available and obtainable
if they are to be used. The pedigree of a code, while it
does not prevent the use of older versions, may imply
that newer versions should be used. Undocumented
codes would impose different emphasis on some of the
other criteria used in the evaluation. These and other
similar data will often control whether or not a code is
used at all rather than how a code is applied to model
a given problem.
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Time Dependence
Transient/ Steady State
Figure 5-2. General Classification of Selection Criteria
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5.2.2 Criteria Based on Phase in the Remedial
Process
In general, regardless of the nature of the on-site
contamination or the regulations being followed, the
remedial process for contaminated sites may generally
be divided into three discrete phases: the scoping
phase, the site characterization phase, and the
remediation phase.
The overall remedial process begins with the scoping
phase, which is designed to assess the existing and
potential risks that the contaminated site poses to
human health and to the environment, and to develop
site characterization plans. The objectives of the site
characterization phase are to obtain sufficient
information to support dose and risk assessment and to
provide specific-site data required to identify feasible
remedies and remedial action goals. The final phase
of the remedial process is the selection,
implementation, and evaluation of a remedy. In each
phase of the remedial process, some information is
available to assist in code selection. In the early
stages, only broad-based decisions canbe supported by
the available data. However, as the process continues,
the available information becomes more detailed, and
the code selection can be based upon very specific
criteria dictated by the following factors:
! Modeling objectives
! Waste characteristics
! Hydrogeological characteristics
! Fate and transport processes
! Fluid and flow conditions
! Local land use and demography
The influence that these criteria have on code selection
is fully described in Sections 3 and 4.
5.2.3 Criteria Based on Waste and Site
Characteristics
Section 4 presents a detailed description of how
specific waste and site characteristics influence code
selection. This section summarizes these points within
the context of completing Table 5-1.
Transport of radionuclides through subsurface
materials is influenced by the physical and chemical
nature of both the transporting media (usually water)
and the medium through which flow occurs (usually
soil or rock). Criteria used to select or evaluate models
will be related to those processes that control the rate
of flow of water through earth materials and those
processes that either remove or deliver materials to
water as it flows through earth materials. Subsurface
flow is controlled by two master variables, hydraulic
conductivity and driving force, and modified by the
variability or continuity among those two variables.
The hydraulic conductivity of porous or fractured
subsurface materials is determined by the volumetric
extent of voids or porosity within the material and the
ease or rate with which fluids can move from one void
to another. Flow within and between void spaces is a
function of the properties of the fluid and the
interaction of that fluid with the walls of the pore
spaces. Since most ground-water flow consists of the
movement of dilute water solutions at very low
velocity, changes in fluid properties generally can be
ignored.
The properties of the media through which the water
flows and which are of overwhelming significance in
controlling the velocity, direction, and quantity of flow
are the relative degree of saturation of the materials,
and the relative importance of fractured versus porous
media flow. These site characteristics can generally be
determined from a study of the type of soil and rock
underlying a site.
The driving force, summed up within the concept of
hydraulic head, for moving a fluid through subsurface
materials is a combination of gravity and any external
force applied to the ground-water flow system, such as
areal recharge.
The factors that control flow through subsurface
materials can be either uniformly or non-uniformly
distributed. When they are uniformly distributed, a
number of simplifying assumptions can be made about
the nature of flow and transport. These simplifying
assumptions have a great influence on the application
of a mathematical model. When subsurface material
properties are anisotropic and/or inhomogeneous, the
direction and rate of flow will vary with position.
These site characteristics alone have a marked effect
on differentiating among codes which tend to be
relatively simple and generalized and those that tend
to be relatively complex and focused.
As solutions move through the spaces within
subsurface materials, solutes may either be added to or
removed from that solution. Which solutes are
removed or added, and the quantity and rate at which
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they are added or removed, is controlled by the
geochemical nature of the solution and subsurface
matrix. These geochemical process may be very
complex, and their understanding may require an
extensive base of physical and chemical data which are
rarely available. Because of their complexity,
geochemical models are generally developed as stand-
alone modules that assume equilibrium (i.e.,
instantaneous reactions) and run independently of flow
and transport models. The site characteristics that will
trigger the requirement to utilize geochemical
modeling are unusual subsurface chemistry such as
sharp variations in chemical conditions (e.g., redox,
pH) within soils and rocks.
Most subsurface transport models lump the effects of
all geochemical reactions into the concept of the
distribution coefficient (Kd) or related retardation
factors because, without assuming any retardation,
there would be a tendency to over-estimate the mobility
of certain highly reactive radionuclides. There is,
however, a very wide range of experimental- and field-
determined values for distribution and retardation
coefficients, and, in practice, as with so many other
characteristics, these parameters are usually best
determined on a site-specific basis. At many sites, it
may be unknown whether predicted changes in the
concentration of radionuclides in ground water can be
adequately explained by the simplifying assumptions
that underlay the Kd concept. As the assumption of a
Kd to calculate radionuclide partitioning is
theoretically valid only if: (1) chemical equilibrium
exists among all aqueous species containing the solute;
(2) reversible, linear sorption is the dominant process
controlling exchange of the solute between the
groundwater and the rock; and (3) transport of the
solute by particulates (colloids) is insignificant. The
site characterization program would need to determine
if these assumptions are valid for radioelement
transport in the ground water or if deviations from
these conditions will produce significant errors.
Consequently, focused geochemical modeling and
laboratory studies may be needed to address these
uncertainties.
The conceptual model is the set of hypotheses and
assumptions about the physical characteristics (e.g.,
aquifer properties and boundary type) and the
phenomena (e.g., model of fluid flow) that describes
and postulates the behavior of the actual system. The
approach to formulating an appropriate conceptual
model(s) of the site integrates the generalized
knowledge of physical processes with the available
information. Therefore, a conceptual model provides
a simplifying framework in which information can be
organized and linked to processes that can be
simulated with predictive models.
The mathematical model is the mathematical
representation of the conceptual model. A
mathematical model might include coupled algebraic,
ordinary or partial differential, or integral equations
that approximate the physical processes for a specified
portion of the site conceptual model. The process by
which the input and output of various mathematical
models may be linked to support the conceptual model
in order to meet the modeling objectives also plays an
important role in the selection of a computer code(s).
For example, the conceptual model may include flow
and transport processes in both the unsaturated and
saturated zones, in which case it would be possible to
select one code that would simulate the flow and
transport processes in the unsaturated zone at the
desired level of detail and to use this model output as
input into a second code which is capable of simulating
flow and transport within the saturated zone.
Therefore, the code selection and evaluation process
has to reflect this availability to potentially dissect the
conceptual model into discrete components.
The overall application of this approach will
essentially be reduced to two considerations: (1) each
component of the conceptual model is adequately
described by the mathematical model; and (2) each of
the separate mathematical models has been
successfully integrated to where the sum of the parts is
equal to the whole. The second consideration is more
applicable to the application of the code and will be far
more difficult to evaluate than the first.
Each code, however, should individually meet the
basic criteria which are related to the site
characteristics and which have been outlined as
general components of the conceptual model that need
to be considered when assessing the appropriateness of
a computer code (Figure 5-3).
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SITE RELATED
Source-Term
Characteristics
Aquifer-System
Characteristics
Transport and
Fate Process
Flow Conditions
Time Dependence
Transient/Steady State
What site-related characteristics are described by the code?
Are the physical characteristics described by the code consistent with the conceptual model?
Do assumptions and limitations that are Inherent within the code provide cause for code rejection?
Figure 5-3. Physical, Chemical, and Temporal Site-Related Selection Criteria
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These broad subjects are further broken down into
their individual components both in the table presented
as Appendix D and in the discussion presented in
Sections 3 and 4.
5.2.4
Criteria Based on Code Characteristics
A contaminant fate and transport model results from
the application of a previously written or new
computer code to a specific problem via the collection
of input data and the parameterization of site
characteristics. The resultant model is, therefore, a
merger of a mathematical formulation, solution
methodology, data, and ancillary information which
enhances or controls the use of the model. Therefore,
in addition to selection criteria for the modeling
objectives which were presented in the previous
section, the code evaluation process must also consider
attributes that are integral components of the computer
code(s) including:
Source Code Availability
History of Use
Code Documentation
Code Testing
Hardware Requirements
Code Output
Solution Methodology
Code Dimensionality
The development of selection criteria presented in this
section takes an approach consistent with industry
standards by relying on published reports pertaining to
the quality assurance and quality control in the
development and application of computer codes.
Source Code Availability
To facilitate a thorough review of the generic code,
detailed documentation of the code and its
developmental history is required. Also, the source
code must be available for inspection (Figure 5-4). In
addition, to ensure independent evaluation of the
reproducibility of the verification and validation
results, the computer source code as well as the
compiled version of the code (i.e., computer code in
machine language) should be available for use by the
reviewer, together with files containing the original
test data used in the code's verification and validation.
History of Use
Much of the information needed for a thorough code
evaluation can be obtained from the author or
distributor of the code (Figure 5-4). In fact, inability
to obtain the necessary publications can be an
indication that the code is either not well documented
or that the code is not widely used. In either case, the
inaccessibility of the documentation and related
publications should be strong grounds for deciding that
the code is unacceptable.
The acceptance and evaluation process should rely on
user opinions and published information in addition to
hands-on experience and testing. User opinions are
especially valuable in determining whether the code
functions as documented or has significant errors or
shortcomings. In some instances, users independent of
the developer have performed extensive testing and
bench-marking or are familiar with published papers
documenting the use of the code. Users will also have
first-hand knowledge about how easy it is to use the
code and what level of experience is required.
Quality Assurance
It is recommended that code selection criteria be
closely tied to the quality assurance criteria which were
folio wed during the development of the computer code.
These criteria will be associated with the adequacy of
the code testing and documentation (Figure 5-5).
Quality assurance in modeling is the procedural and
operational framework put in place by the organization
managing the modeling study, to assure technically
and scientifically adequate execution of all project
tasks included in the study, and to assure that all
modeling-based analysis is verifiable and defensible
(TAY85).
The two major elements of quality assurance are
quality control and quality assessment. Quality control
refers to the procedures that ensure the quality of the
final product. These procedures include the use of
appropriate methodology in
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CODE RELATED
Source Code
Availability
Public Domain
Commercially
Available
Project Specific
Is source code available for independent review?
Is executable code available for Independent review?
History of Use
Figure 5-4. Source Code Availability and History of Use Selection Criteria
5-11
Is code user friendly?
Has code been used
on similar problems?
Have previous users
been surveyed?
Are published reports
available?
Are code authors
available for consultation?
-------
CODE RELATED
Quality Assurance
Adequacy of
Documentation
Code Development
Report
Adequacy of
Testing
_L
Is report properly
documented?
Verification
Is verification process
adequately described?
Field Testing
Was testing against
problems of similar
complexity completed?
Extended model description
Model Input data description and format
Type of output data provided
Code execution preparation Instructions
Sample model runs
Trouble shooting guide
Functional description of the model
Model input and output data
Code verification and validation Information
Model specifications
Model description
Flow charts
Descriptions of routines
Database description
Source listing
Error messages
Were any fie Id
tests performed?
Over what scales?
Over what time frame?
Which processes have
been validated?
Figure 5-5. Quality Assurance Selection Criteria
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developing and applying computer simulation codes,
adequate verification and validation procedures, and
proper usage of the selected methods and codes
(HEI92). To monitor the quality control procedures
and to evaluate the quality of the studies, quality
assessment is applied (HEI89).
Software quality assurance (SQA) consists of the
application of procedures, techniques, and tools
through the software life cycle, to ensure that the
products conform to pre-specified requirements
(BRY87). This requires that in the initial stage of the
software development project, appropriate SQA
procedures (e.g., auditing, design inspection, code
inspection, error-prone analysis, functional testing,
logical testing, path testing, reviewing, walk-through),
and tools (e.g., text-editors, software debuggers, source
code comparitors, language processors) need to be
identified and the software design criteria be
determined (HEI92).
Quality assurance for code development and
maintenance implies a systematic approach, starting
with the careful formulation of code design objectives,
criteria and standards, followed by an implementation
strategy. The implementation strategy includes the
design of the code structure and a description of the
way in which software engineering principles will be
applied to the code. In this planning stage, measures
are to be taken to ensure complete documentation of
code design and implementation, record keeping of the
coding process, description of the purpose and
structure of each code segment (functions,
subroutines), and record-keeping of the code
verification process.
Records for the coding and verification process may
include: a description of the fundamental algorithms
describing the physical process(es) which are to be
modeled; the means by which the mathematical
algorithms have been translated into computer code
(e.g., Fortran); results of discrete checks on the
subroutines for accuracy; and comparisons among the
codes' numerical solutions with either analytical or
other independently verified numerical solutions.
Code verification or testing ensures that the underlying
mathematical algorithms have been correctly
translated into computer code. The verification
process varies for different codes and ranges from
simply checking the results of a plotting routine to
comparing the results of the computer code to known
analytical solutions or to results from other verified
codes.
Traceability describes the ability of the computer
analyst to identify the software which was used to
perform a particular calculation, including its name,
date, and version number, while retrievability refers to
the availability of the same version of the software for
further use.
Code Documentation
Detailed guidelines for the preparation of
comprehensive software documentation are given by
the Federal Computer Performance Evaluation and
Simulation Center (FED81). This publication
discusses the structure recommended for four types of
manuals providing model information for managers,
users, analysts and programmers. According to
FEDSIM (1981), the manager's summary manual
should contain a model description, model
development history, an experimentation report, and a
discussion of current and future applications.
Currently, ASTM (American Society for Testing and
Materials) is developing a standard ground-water code
description for this specific purpose (HEI92).
As discussed in van der Heijde (1992), the code
documentation should include a description of the
theoretical framework represented by the generic
model on which the code is based, code structure and
language standards applied, and code use instructions
regarding model setup and code execution parameters.
Furthermore, the documentation should also include a
complete treatment of the equations on which the
generic model is based, the underlying mathematical
and conceptual assumptions, the boundary conditions
that are incorporated in the model, the method and
algorithms used to solve the equations, and the
limiting conditions resulting from the chosen
approach. The documentation should also include
user's instructions for implementing and operating the
code, and preparing data files. It should present
examples of model formulation (e.g., grid design,
assignment of boundary conditions), complete with
input and output file descriptions and include an
extensive code verification and validation or field
testing report. Finally, programmer-orientated
documentation should provide instructions for code
modification and maintenance.
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An integral part of the code development process is the
preparation of the code documentation. This
documentation of QA in model development consists
of reports and files pertaining to the development of
the model and should include (HEI92):
A report on the development of the code
including the (standardized and approved)
programmer's bound notebook containing
detailed descriptions of the code
verification process;
Verification report including verification
scenarios, parameter values, boundary and
initial conditions, source-term conditions,
dominant flow and transport processes;
Orientation and spacing of the grid and
justification;
Time-stepping scheme and justification;
Changes and documentation of changes
made in code after baselining;
Executable and source code version of
baselined code;
Input and output (numerical and
graphical) for each verification run;
Notebook containing reference material
(e.g., published papers, laboratory results,
programmers rationale) used to formulate
the verification problem.
Furthermore, the software should be documented in
sufficient detail to (GAS79):
record technical information that enables
system and program changes to be made
quickly and effectively;
enable programmers and system analysts,
other than software originators, to use and
to work on the programs;
assist the user in understanding what the
program is about and what it can do;
increase program sharing potential;
facilitate auditing and verification of
program operations;
provide managers with information to
review at significant developmental
milestones so that they may independently
determine that project requirements have
been met and that resources should
continue to be expended;
reduce disruptive effects of personnel
turnover;
facilitate understanding among managers,
developers, programmers, operators, and
users by providing information about
maintenance, training, and changes in and
operation of the software;
inform other potential users of the
functions and capabilities of the software,
so that they can determine whether it
serves their needs.
The user's manual should, at a minimum, consist of:
an extended code description;
code input data description and format;
type of output data provided;
code execution preparation instructions;
sample model runs;
trouble shooting guide; and
contact person/affiliated office.
The programmer's manual should, at a minimum,
include:
code specifications;
code description;
flow charts;
descriptions of routines;
data-base description;
source listing;
error messages; and
contact person/affiliated office.
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The analyst's manual should, at a minimum, present:
a functional description of the code;
code input and output data;
code verification and validation
information; and
contact person/affiliated office.
The code itself should be well structured and internally
well documented; where possible, self-explanatory
parameter, variable, subroutine, and function names
should be used.
Code Testing
Before a code can be used as a planning and decision-
making tool, its credentials must be established
through systematic testing of the code's correctness and
evaluation of the code's performance characteristics
(HEI89). Of the two major approaches available, the
evaluation or review process is rather qualitative in
nature, while code-testing results can be expressed
using quantitative performance measures.
Code testing (or code verification) is aimed at
detecting programming errors, testing embedded
algorithms, and evaluating the operational
characteristics of the code through its execution on
carefully selected example test problems and test data
sets. ASTM84 defines verification as the examination
of the numerical technique in the computer code to
ascertain that it truly represents the conceptual model,
and that there are no inherent problems with obtaining
a correct solution.
At this point, it is necessary to point out the distinction
between generic simulation codes based on an
analytical solution of the governing equation(s)
(Appendix C) and codes that include a numerical
solution. Verification of a coded analytical solution is
restricted to comparison with independently calculated
results using the same mathematical expression, i.e.,
manual calculations, using the results from computer
programs coded independently by third party
programmers. Verification of a code formulated with
numerical methods might take two forms: (1)
comparison with analytical solutions, and (2) code
intercomparison between numerically based codes,
representing the same generic simulation model, using
synthetic data sets.
It is important to distinguish between code testing and
model testing. Code testing is limited to establishing
the correctness of the computer code with respect to
the criteria and requirements for which it is designed
(e.g., to represent the mathematical model). Model
testing (or model validation) is more inclusive than
code testing, as it represents the final step in
determining the validity of the quantitative
relationships derived for the real-world system the
model is designed to simulate.
Attempts to validate models must address the issue of
spatial and temporal variability when comparing
model predictions with limited field observations. If
sufficient field data are obtained to derive the
probability distribution of contaminant concentrations,
the results of a stochastic model can be compared
directly. For a deterministic model, however, the
traditional approach has been to vary the input data
within its expected range of variability (or uncertainty)
and determine whether the model results satisfactorily
match historical field measured values. This code-
testing exercise is sometimes referred to as history
matching.
Konikow and Bredehoeft (KON92) present a
compelling argument that computer models cannot be
truly validated but can only be invalidated. As
reported by Hawking (HAW88), any physical theory is
only provisional, in the sense that it is only a
hypothesis that can never be proven. No matter how
many times the results of the experiments agree with
some theory, there is never complete certainty that the
next test will not contradict the theory. On the other
hand, a theory can be disproven by finding even a
single observation that disagrees with the predictions
of the theory.
From a philosophical perspective, it is difficult to
develop selection criteria for a model validation
process which may be intrinsically flawed. However,
the average strategy presented in this chapter provides
some assurance that the code selected has the highest
probability of most accurately representing the
conceptual model.
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Hardware Requirements
In general, hardware requirements should rarely be a
discriminatory factor in the selection of a computer
code (Figure 5-6). However, a number of the available
codes require very sophisticated hardware, not so much
because of the intrinsic requirements of the code but
because the simulated processes may be very complex
and require time-consuming solution methods.
Therefore, hardware requirements should be clearly
identified for the code itself and be consistent with the
hardware available to the user.
Mathematical Solution Methodology
Every ground-water or contaminant transport model is
based upon a set of mathematical equations. Solution
methodology refers to the strategy and techniques used
to solve these equations. In ground-water modeling,
the equations are normally solved for head (water
elevations in the subsurface) and/or contaminant
concentrations.
Mathematical methods can be broadly classified as
either deterministic or stochastic (Figure 5-7).
Deterministic methods assume that a system or process
operates such that the occurrence of a given set of
events leads to a uniquely definable outcome.
Stochastic methods pre-suppose the outcome to be
uncertain and are structured to account for this
uncertainty.
Most stochastic methods are not completely stochastic
in that they often utilize a deterministic representation
of soil processes and derive their stochastic nature
from their representation of inputs and/or spatial
variation of soil characteristics and resulting chemical
movement (i.e., Monte Carlo). While the deterministic
approach results in a specific value of a soil variable
(e.g., solute concentration) at pre-specified points in
the domain, the stochastic approach provides the
probability (within a level of confidence) of a specific
value occurring at any point.
Deterministic methods may be broadly classified as
either analytical or numerical. Analytical methods
usually involve approximate or exact solutions to
simplified forms of the differential equations for water
movement and solute transport. Simple analytical
methods are based on the solution of applicable
differential equations which make a simplified
idealization of the field and give qualitative estimates
of the extent of contaminant transport. Such models
are simpler to use than numerical models and can
generally be solved with the aid of a calculator,
although computers are also used. Analytical models
are restricted to simplified representations of the
physical situations and generally require only limited
site-specific input data. They are useful for screening
sites and scoping the problem to determine data needs
or the applicability of more detailed numerical models.
Analytical solutions are used in modeling
investigations to solve many different kinds of
problems. For example, aquifer parameters are
obtained from aquifer pumping and tracer tests
through the use of analytical models, and ground-water
flow and contaminant transport rates can also be
estimated with the use of analytical models.
Numerical models provide solutions to the differential
equations describing water movement and solute
transport using numerical methods such as finite
differences and finite elements. Numerical methods
account for complex geometry and heterogenous
media, as well as dispersion, diffusion, and chemical
retardation processes (e.g., sorption, precipitation,
radioactive decay, ion exchange, degradation). These
methods almost always require a digital computer,
greater quantities of data than analytical modeling, and
experienced modelers.
The validity of the results from mathematical models
depends strongly on the quality and quantity of the
input data. Stochastic, numerical, and analytical codes
have strengths and weaknesses inherent within their
formulations, all of which need to be considered prior
to their selection.
Code Output
One aspect of the computer code that is frequently
ignored in the selection process is the form of the
model output (Figure 5-8). It is true, however, that in
most instances the actual output can be fashioned into
the desired format, provided the model itself is
consistent with required output (e.g., output in three
dimensions cannot be obtained with a two-dimensional
model).
5-16
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Micro/ PC Based
CODE RELATED
Hardware Requirements
Mini/Workstation
Based
Memory Requirements
Operating System
(e.g., UNIX, DOS)
Supercomputer
Figure 5-6. Hardware Requirements Selection Criteria
5-17
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CODE RELATED
Mathematical
Solution Methodology
Deterministic
Analytical
Stochastic
1
Numerical
Monte Carlo
Moment Analysis
Are overall solution techniques appropriate for specific problems?
Are numerical efficiency and stability achieved?
Is mass balance maintained?
Figure 5-7. Mathematical Solution Methodology Acceptance Criteria
-------
CODE RELATED
Code Output
Contaminant Concentration
as a Function of Distance
from Surface
Contaminant Plume
Specified Source Rate
Mass Balance
Error Messages
Matrix Formulation Type Information
Combined Cumulative Distribution
Functions of Release Probability
Dose and/or Concentration
Breakthrough Curves at Selected
Points Over Time
As an Average or as Discrete Values
at Selected Points or Cells
Continuously Distributed in
Space
As a Function of Depth from
Surface
Figure 5-8. Code Output Selection Criteria
5-19
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In general, the model output is expressed in terms of
hydraulic head, pressure, velocities, or solute
concentrations. The spatial coverage of parameter
output values is either dependent on the frequency of
nodal spacing (numerical) or on the number of
specified x and y coordinates (analytical) which are
included in the model input files. Model output will
also vary due to the inherent nature of the code itself.
For example, codes that simulate movement in the
unsaturated zone generally produce saturationprofiles.
These profiles indicate the percentage of the pore space
that is filled with water, whereas saturated zone codes
have no need forthis capability because all of the pores
below the water table are assumed to be filled
completely with water. The single most important
code selection criteria, relative to the model output,
would be that the code provides mass-balance
information. A mass-balance determination is a check
to ensure that the amount of water or contaminant
mass entering the system equals the amount exiting the
system plus the change in the quantity stored in the
system. If there is a significant discrepancy in the
model's mass balance, something may be wrong with
the numerical solution, although errors in the mass
balance may also indicate problems with the mass-
balance formulation itself. Therefore, mass-balance
information not only provides a check on the
mathematical formulations within the code, but also
assists in ensuring that input parameter conversions
and other errors have not been made. It is not
uncommon for codes that do include mass-balance
output to provide information (e.g., fluxes, heads) on
specific boundaries as well as the source term, all of
which can be used in the interpretation and evaluation
of the predicted flow and solute transport directions
and rates.
Code Dimensionality
The determination as to the number of dimensions that
a code should be capable of simulating is based
primarily upon the modeling objectives and the
dimensionality of the processes the code is designed to
simulate (Figure 5-9).
In determining how many dimensions are necessary to
meet the objectives, it becomes necessary to gain a
basic understanding of how the physical processes
(e.g., ground-water flow and transport) are affected by
the exclusion or inclusion of an additional dimension.
It should be kept in mind that the movement of ground
water and contaminants is usually controlled by
advective and dispersive processes which are
inherently three-dimensional. Advection is more
responsible for the length of time (i.e., travel time) it
takes for a contaminant to travel from the source term
to a downgradient receptor, while dispersion directly
influences the concentration of the contaminant along
its travel path. This fact is very important in that it
provides an intuitive sense forthe effect dimensionality
has on contaminant migration rates and
concentrations.
As a general rule, the fewer the dimensions, the more
the model results will over-estimate concentrations and
under-estimate travel times. In a model with fewer
dimensions, predicted concentrations will generally be
greater because dispersion, which is a three-
dimensional process, will be dimension limited and
will not occur to the same degree as it actually would
in the field. Similarly, predicted travel times will be
shorter than the actual travel time, not because of a
change in the contaminant velocities but because a
more direct travel path is assumed. Therefore, the
lower dimensionality models tend to be more
conservative in their predictions and are frequently
used for screening analyses.
One-dimensional simulations of contaminant transport
usually ignore dispersion altogether, and
contamination is assumed to migrate solely by
advection, which may result in a highly conservative
approximation. Vertical analyses in one dimension are
generally reserved for evaluating flow and transport in
the unsaturated zone. Two-dimensional analyses of an
aquifer flow system can be performed as either a
planar representation, where flow and transport are
assumed to be horizontal (i.e., longitudinal and
transverse components), or as a cross section where
flow and transport components are confined to vertical
and horizontal components.
In most instances, two-dimensional analyses are
performed in an areal orientation, with the exception
of the unsaturated zone, and are based on the
assumption that most contaminants enter the saturated
system from above and that little vertical dispersion
occurs. However, a number of limitations accompany
two-dimensional planar simulations. These include
the inability to simulate multiple layers (e.g., aquifers
and aquitards) as well as any partial penetration
effects. Furthermore, because vertical
5-20
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CODE RELATED
Dimensionality
Have critical dimensions of the
dominant physical processes
been identified?
Is code capable of simulating the identified
processes in required number
of dimensions?
Figure 5-9. Code Dimensionality Selection Criteria
5-21
-------
components of flow are ignored, an artificial lower
boundary on contaminant migration has been
automatically assumed which may or may not be the
case.
A two-dimensional formulation of the flow system is
frequently sufficient for the purposes of risk
assessment provided that flow and transport in the
contaminated aquifer are essentially horizontal. The
added complexities of a site-wide, three-dimensional
flow and transport simulation are often believed to
outweigh the expected improvement in the evaluation
of risk. Complexities include limited site-wide
hydraulic head and lithologic data with depth and
significantly increased computational demands.
Quasi-three-dimensional analyses remove some of the
limitations inherent in two-dimensional analyses.
Most notably, quasi-three-dimensional simulations
allowforthe incorporation of multiple layers; however,
flow and transport in the aquifers are still restrained to
longitudinal and transverse horizontal components,
whereas flow and transport in the aquitards are even
further restricted to vertical flow components only.
Although partial penetration effects still cannot be
accommodated in quasi-three-dimensional analyses,
this method can sometimes provide a good
compromise between the relatively simplistic two-
dimensional analysis and the complex, fully three-
dimensional analysis. This is the case, particularly if
vertical movement of contaminants or recharge from
the shallow aquifer through a confining unit and into
a deeper aquifer is suspected.
Fully three-dimensional modeling generally allows
both the geology and all of the dominant flow and
transport processes to be described in three
dimensions. This approach usually affords the most
reliable means of predicting ground-water flow and
contaminant transport characteristics, provided that
sufficient representative data are available for the site.
Although the intrinsic dimensionality of the code
should be an important consideration relative to the
acceptance or rejection of the code, this determination
will also be closely tied to the code application and
modeling objectives.
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NRC90a Nuclear Regulatory Commission, 1990. "Performance Assessment Methodologies for Low-Level
Waste Facilities," Prepared by Sandia National Laboratory, NUREG/CR-5532, July 1990.
PAR92 Pardi, R.R., Daum, M.L., and Moskowitz, P.O., 1992. Environmental Characteristics of EPA. NRC.
and DOE Sites Contaminated with Radioactive Substances. U. S. Environmental Protection Agency,
Office of Radiation Programs, Washington, D.C.
SHE90 Sheppard, M.I., and E.L. Gershey, 1990. "Default Solid Soil/Liquid Partition Coefficients, Kds, for
Four Major Soil Types: A Compendium," Health Physics. 59 (4):471, October 1990.
TAY85 Taylor, J.K., 1985. What is Quality Assurance? In: J.K. Taylor and T.W. Stanley (eds.), Quality
Assurance for Environmental Measurements, pp. 5-11. ASTM Special Technical Publication 867,
Am. Soc. for Testing and Materials, Philadelphia, Pennsylvania.
ZHE90 Zheng, C., 1990. A Modular Three-Dimensional Transport Model for Simulation of Advection,
Dispersion, and Chemical Reactions of Contaminants in Ground-Water Systems, Prepared for the
United States Environmental Protection Agency, Robert S. Kerr Environmental Research Laboratory,
Ada, Oklahoma.
Ref-3
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BIBLIOGRAPHY
Barney, G.S., J.D. Navratil, and W.W. Schultz, 1984. Geochemical Behavior of Disposed Radioactive Waste.
American Chemical Society, Washington, D.C.
Bear, J., 1979. Hydraulics of Ground Water. McGraw-Hill Book Company.
Boonstra, J. and N.A. de Ridder, 1981. Numerical Modeling of Ground-Water Basins. ILRI Publication 29.
de Marsily, G., 1986. Quantitative Hydrogeology. Ground-Water Hydrology for Engineers, Academic Press, Inc.
Drever, J.I., 1982. The Geochemistry of Natural Waters. Prentice-Hall Inc., Englewood Cliffs, N.J.
Environmental Protection Agency, 1985. "Modeling Remedial Actions at Uncontrolled Hazardous Waste Sites,"
EPA/540/2-85/001, Office of Solid Waste and Emergency Response and Office of Research and Development.
Environmental Protection Agency, 1987. "The Use of Models in Managing Ground-Water Protection Programs,"
EPA/600/8-87/003, Robert S. Kerr Environmental Research Laboratory.
Environmental Protection Agency, 1988. "Groundwater Modeling: An Overview and Status Report," EPA/600/2-
89/028, Robert S. Kerr Environmental Research Laboratory.
Environmental Protection Agency, 1989. "Predicting Subsurface Contaminant Transport and Transformation:
Considerations for Model Selection and Field Validation," EPA/600/2-89/045, Robert S. Kerr Environmental
Research Laboratory.
Environmental Protection Agency, 1992. "Quality Assurance and Quality Control in the Development and
Application of Ground-Water Models," EPA/600/R-93/011, Office of Research and Development.
Environmental Protection Agency, 1992. "Ground-water Modeling Compendium," EPA-500-B-92-006, Office of
Solid Waste and Emergency Response.
Environmental Protection Agency, 1993. "Compilation of Ground-Water Models," EPA/600/R-93/118, Office of
Research and Development.
Fetter, C.W., 1993. Contaminant Hydrogeology. Macmillan Publishing Company.
Freeze, R.A. and J.A. Cherry, 1979. Ground Water. Prentice-Hall, Inc.
Hern, S.C. and S.M. Melancon, 1986. Vadose Zone Modeling of Organic Pollutants. Lewis Publishers, Inc.
Chelsea, Michigan.
Istok, J., 1989. Ground-Water Modeling by the Finite Element Method. Water Resources Monograph 13,
American Geophysical Union.
Jorgensen, S.E., 1984. Modelling the Fate and Effect of Toxic Substances in the Environment. Developments in
Environmental Modelling, 6.
Jury, W.A., W.R. Gardner and W.H. Gardner, 1991. Soil Physics. Fifth Edition. John Wiley & Sons, Inc.
Bib-1
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Liggett, J.A., and P.L-F. Liu, 1983. The Boundary Integral Equation Method for Porous Media Flow. School of
Civil and Environmental Engineering, Cornell University, N.Y.
Matthess G., 1982. The Properties of Ground Water. John Wiley & Sons, Inc.
Resources Management and Information Staff, 1992. Ground-Water Modeling Compendium OSWER Models
Management Initiative: Pilot Project on Ground-Water Modeling. Office of Solid Waste and Emergency
Response.
Thomas, R.G., 1973. "Groundwater Models," Food and Agriculture Organization of the United Nations, Rome,
FAO Irrigation and Drainage Paper.
Wang, H.F. andM.P. Anderson, 1982. Introduction to Ground-Water Modeling. Finite Difference and Finite
Element Methods. W.H. Freeman and Company.
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APPENDIX A
GLOSSARY
A-l
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GLOSSARY
ACTINIDES - Elements 90 through 103.
ADSORPTION - Physical attraction and adhesion of gas, vapor, or dissolved molecules to the surface of solids
without chemical reaction.
ADVECTION - The process by which solutes are transported by the bulk motion of flowing ground water.
ALLUVIAL FLOODPLAIN - The lowland adjacent to a river, usually dry but subject to flooding when the river
overflows its banks. It is that flat area constructed by the present river in the present climate. It is built of
alluvium carried by the river during floods and deposited in the sluggish water beyond the influence of the swiftest
current.
ANALYTICAL MODEL - A model based on known initial and boundary conditions which incorporates a
continuous exact solution of a simple flow or solute transport equation such as Darcy's Law. Analytical models are
ordinarily restricted to conditions of homogeneous, isotropic flow, and transport.
ANION EXCLUSION - Negatively charged rock surfaces can affect the movement of anions, by either retarding
the movement of anions by not allowing negatively charged radionuclides to pass through the pore opening or by
enhancing the transport of ions by restricting the anion movement to the center of the pore channel where ground-
water velocities are higher.
ANISOTROPIC - Having some physical property that varies with direction of flow.
AQUIFER - A unit of porous material capable of storing and transmitting appreciable quantities of water to wells.
AQUITARD - A saturated, but poorly permeable bed, formation, or group of formations that can store ground
water and also transmit it slowly from one aquifer to another.
ARTESIAN WELL - A well deriving its water from a confined aquifer in which the water level in the casing
stands above the top of the confined aquifer.
BASALT - A general term for dark-colored iron- and magnesium-rich igneous rocks, commonly extrusive, but
locally intrusive. It is the principal rock type making up the ocean floor.
BEDROCK - A general term for the rock, usually solid, that underlies soil or other unconsolidated material.
BIOFIXATION - The binding of radionuclides to the soil/organic matrix due to the action of some types of
microorganisms and plants, thus affecting mobility of the radionuclide.
BULK DENSITY - The mass or weight of oven-dry soil per unit bulk volume, including air space.
CALIBRATION - The process by which a set of values for aquifer parameters and stresses is found that
approximates field-measured heads and flows. It is performed by trial-and-error adjustment of parameters and
boundary conditions or by using an automated parameter estimation code.
CAPTURE ZONE - The portion of the flow system that contributes water to a well or a surface water body such
as a river, ditch, or lake.
A-2
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CHAIN DECAY - Form of radioactive decay in which several daughter products may be produced before the
parent species decays to a stable element.
CLAY - (Clay particles are mineral particles < 0.002 mm. in diameter). In the grading of soils by texture, clay is
the extreme of fineness.
CONFINED AQUIFER - An aquifer which is overlain by a unit of porous material that retards the movement of
water.
CURVILINEAR ELEMENTS - Specialized elements used by finite-element computer codes that can be spatially
deformed to mimic the elevations of the upper and lower surfaces of the hydrogeologic units.
DARCY'S LAW - A derived equation that can be used to compute the quantity of water flowing through an
aquifer assuming that the flow is laminar and inertia can be neglected.
DETERMINISTIC MODEL - A model whose output is fixed by the mathematical form of its equations and the
selection of a single value for each input parameter.
DIP - The angle to the horizontal (slope) that a geologic unit may have.
DISCHARGE - The volume of water flowing in a stream or through an aquifer past a specific point in a given
period of time.
DISPERSION - A mixing phenomenon linked primarily to the heterogeneity of the microscopic velocities inside
the porous medium.
DISTRIBUTION COEFFICIENT - The slope of a linear Freundlich isotherm.
EFFECTIVE POROSITY - The volume of the void spaces through which water or other fluids can travel in a
rock or sediment divided by the total volume of the rock or sediment.
FACILITATIVE TRANSPORT - A term used to describe the mechanism by which radionuclides may couple
with either naturally occurring material or other contaminants and move at much faster rates than would be
predicted by their respective distribution coefficients.
FAULT - A fracture or a zone of fractures along which there has been displacement of the sides relative to one
another parallel to the fracture.
FINITE DIFFERENCE - A particular kind of a digital computer model based upon a rectangular grid that sets
the boundaries of the model and the nodes where the model will be solved.
FINITE ELEMENT - A digital ground-water flow model where the aquifer is divided into a mesh formed of a
number of polygonal cells.
FLOCCULATION - The agglomeration of finely divided suspended solids into larger, usually gelatinous,
particles; the development of a "floe" after treatment with a coagulant by gentle stirring or mixing.
FRACTURED LITHOLOGY - Porous media which is dissected by fractures.
FREUNDLICH ISOTHERM - An empirical equation that describes the amount of solute adsorbed onto a soil
surface.
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GEOCHEMICAL FACIES - A unit of material of similar physical properties that was deposited in the same
geologic environment.
GROUT CURTAIN - An underground wall designed to stop ground-water flow; can be created by injecting grout
into the ground, which subsequently hardens to become impermeable.
GROUTING - The operation by which grout is placed between the casing and the sides of the well bore to a
predetermined height above the bottom of the well. This secures the casing in place and excludes water and other
fluids from the well bore.
HETEROGENOUS - Pertaining to a substance having different characteristics in different locations.
HYDRAULIC CONDUCTIVITY - A coefficient of proportionality describing the rate at which water can move
through a permeable medium. The density and kinematic viscosity of the water must be considered in determining
hydraulic conductivity. The rate of flow of water in unit volume per unit of time through a unit cross section of
area of geologic material under a unit hydraulic gradient, at the prevailing temperature.
HYDRAULIC GRADIENT - The change in total head with a change in distance in a given direction. The
direction is that which yields a maximum rate of decrease in head.
HYDRODYNAMIC DISPERSION - The process by which ground water containing a solute is diluted with
uncontaminated ground water as it moves through an aquifer.
HYDROFRACTURING - The process in which fluid is added to an aquifer at sufficient pressures to where the
pore pressure in the rock causes the rocks to fracture.
HYDROSTATIGRAPHIC UNIT - A formation, part of a formation, or group of formations in which there are
similar hydrologic characteristics allowing for grouping into aquifers or confining layers.
HYSTERESIS - A term which describes the fact that wetting and drying curves for a certain soil (pressure head
versus volumetric water content) under partially saturated conditions, are not the same.
IMMISCIBLE - Substances that do not mix or combine readily.
IN-SITU VITRIFICATION - Process by which electrodes are used to heat the soil-waste matrix to temperatures
high enough to melt soils and destroy organics by pyrolysis.
INTRINSIC PERMEABILITY - Pertaining to the relative ease with which a porous medium can transmit a
liquid under a hydraulic or potential gradient. It is a property of the porous medium and is independent of the
nature of the liquid or the potential field.
INVERSE MODEL - The model in which values of the parameters and the hydrologic stresses are determined
from the information about heads.
ION EXCHANGE - A process by which an ion in a mineral lattice is replaced by another ion that was present in
an aqueous solution.
LANGMUIR ISOTHERM - An empirical equation that describes the amount of solute adsorbed onto a soil
surface.
LAYERED LITHOLOGY - Interbedded geologic units (e.g., sand, clay, gravel).
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LEACH - The removal of soluble chemical elements or compounds by the passage of water through the soil.
LEACHATE - Water that contains a high amount of dissolved solids and is created by liquid seeping from a
landfill.
LIMESTONE - A sedimentary rock consisting chiefly of calcium carbonate, primarily in the form of the mineral
calcite.
LITTORAL - Pertaining to the ocean environment between the high tide and the low tide.
LOADING RATES - The rate at which contaminants and/or water enters the model domain.
LOW PERMEABILITY BARRIERS - Vertical or horizontal obstructions that are of sufficiently low
permeability to retard significantly the migration of water and/or contaminants.
MACROPORES - Large or noncapillary pores. The pores, or voids, in a soil from which water usually drains by
gravity. Is differentiated from a micropore, or capillary pore space, which consists of voids small enough that
water is held against gravity by capillarity. Sandy soils have a large macropore, or noncapillary pore space and a
small micropore, or capillary, pore space. Non-granular clayey soils are just the reverse.
MATRIX DIFFUSION - The diffusion of radionuclides from water moving within fractures, or coarse-grained
material, into the rock matrix or finer grained clays.
METAMORPHIC ROCK - Any rock derived from preexisting rocks by mineralogical, chemical, and/or
structural changes, essentially in the solid state, in response to marked changes in temperature, pressure, shearing
stress, and chemical environment, generally at depth in the Earth's crust.
MOLECULAR DIFFUSION - Dispersion of a chemical caused by the kinetic activity of the ionic or molecular
constituents.
NON-AQUEOUS PHASE LIQUIDS (NAPL) - Liquids that are immiscible in water.
NUMERICAL MODEL - One of five methods (finite-difference, finite element, integrated finite difference,
boundary integral equation method, and analytical elements) used to approximate by means of algebraic equations
the solution of the partial differential equations (governing equation, boundary, and initial conditions) that
comprise the mathematical model. Numerical models can be used to describe flow under complex boundary
conditions and where aquifer parameters vary within the model area.
ORGANIC COMPLEXATION - The formation of organic complexes by the combination of organic material or
radionuclides.
PARTICLE TRACK - The movement of infinitely small imaginary particles placed in the flow field.
PARTITIONING - The process by which a contaminant, which was originally in solution, becomes distributed
between the solution and the solid phase.
PERCHED WATER - Unconfined ground water separated from an underlying main body of ground water by an
unsaturated zone.
POROUS MEDIA - Rocks that are not dissected by discrete features (e.g., macropores, fractures).
A-5
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PROPRIETARY - A code in which the ownership rights are held by a company or organization.
RADIAL FLOW - The flow of water in an aquifer toward a vertically oriented well.
RADIOACTIVE DECAY - The change of a nucleus into another nucleus (or a more stable form of the same
nucleus) by the loss of a small particle or a gamma ray photon.
RECHARGE - The addition of water to the zone of saturation; also, the amount of water added.
RETARDATION FACTOR/COEFFICIENT - A measure of the capability of adsorption within the porous
media to impede the movement of a particular radionuclide being carried by the fluid.
SANDSTONE - A sedimentary rock composed of abundant rounded or angular fragments of sand set in a fine-
grained matrix (silt or clay) and more or less firmly united by a cementing material.
SATURATED ZONE - The zone in which the voids in the rock or soil are filled with water at a pressure greater
than atmospheric. The water table is the top of the saturated zone in an unconfined aquifer.
SECOND AY MINERALIZATION - Mineralization that occurred later than the rock enclosing it.
SEDIMENTARY ENVIRONMENT - An environment in which the rocks are formed by the accumulation and
cementation of mineral grains transported by wind, water, or ice to the site of deposition or chemically precipitated
at the site of deposition.
SHALE - A fine-grained sedimentary rock, formed by the consolidation of clay, silt, or mud. It is characterized by
finely laminated structure and is sufficiently indurated so that it will not fall apart on wetting.
SILT - Soil particles between 1/256 and 1/2 mm in diameter, smaller than sand and larger than clay.
SOLUTION FEATURES - An opening resulting from the decomposition of less soluble rocks by water
penetrating pre-existing interstices, followed by the removal of the decomposition products.
SOURCE TERM - The quantity of radioactive material released to the biosphere, usually expressed as activity per
unit time. Source terms should be characterized by the identification of specific radionuclides and their physical
and chemical forms.
SPECIATION - The chemical form of the radionuclide, which can influence its solubility and therefore its rate of
transport by limiting the maximum concentration of the element dissolved in the aqueous phase.
A-6
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APPENDIX B
GROUND-WATER MODELING RESOURCES
B-l
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ELECTRONIC MEDIA-BASED SOURCES OF ASSISTANCE
Bulletin Boards
Access to bulletin boards is made via modem either by direct dialing or through a communication system like TELNET
or TYMNET. Access to most systems is controlled by the use of login protocols and passwords obtained from the
system operator. Examples of existing systems include:
Name: ORB-BBS
Purpose: Information about ORD operations and software available through ORD
Maintained by: U. S. Environmental Protection Agency
Office of Research and Development
Cincinnati, Ohio
Charles W. Gulon
(513) 569-7610 (1200-2400 bps)
(800) 258-9605 (1200-9600 bps)
(513) 569-7700 (1200-9600 bps)
(513)569-7272
Communication Parameters: 1200, 2400, 4800, 9600 - N-8-1
Hours/Cost: 24 hours/7 days - Free
System Operator:
Modem Phone(s):
CEAM
Supports the use of exposure assessment models, especially
those used to model the transport of agricultural chemicals.
U. S. EPA
Office of Research and Development
Athens, Georgia
David Disney
(706) 546-3402
(FTS) 250-3549
(706) 546-3590
(706)546-3136
Communication Parameters: 1200, 2400 - N-8-1
Hours/Cost: 24 hours/7 days - Free
Name:
Purpose:
Maintained by:
System Operator:
Modem Phone(s):
Voice Phone(s):
Name:
Purpose:
Maintained by:
System Operator:
Voice Phone(s):
CSMoS
The Center for Subsurface Modeling Support (CSMoS) provides ground-water modeling
software and services to public agencies and private companies throughout the nation.
U.S. Environmental Protection Agency
Center for Subsurface Modeling Support
R.S. Kerr Environmental Research Laboratory
Dr. David S. Burden
(405) 332-8800
Bulletin Boards (Continued)
B-2
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Name: CLU-IN
Purpose: Current events information for hazardous waste cleanup professionals,
innovative technologies, and access to databases.
Maintained by: U. S. EPA
Office of Solid Waste and Emergency Response
Technology Innovation Office
Washington, D.C.
System Operator: Dan Powell
Modem Phone(s): (301)589-8366
Voice Phone(s): (301) 589-8368
Communication Parameters: 1200, 2400 - N-8-1
Hours/Cost: 24 hours/7 days - Free
Name: USGS BBS
Purpose: General information from USGS
Maintained by: U. S. Geological Survey
System Operator:
Modem Phone(s): (703)648-7127
(703) 648-4168
Voice Phone(s): (703) 648-7000
Communication Parameters:
Hours/Cost: CD-ROM conference is Free
Name: ESDD
Purpose: Earth Science Data Directory - list of nationwide databases of earth
science data
Maintained by: U. S. Geological Survey
Reston, Virginia
System Operator: Joe Kemper
Modem Phone(s): (703)648-4100
(703) 648-4200
Voice Phone(s): (703) 648-7112\
Communication Parameters: 300, 1200, 2400, 9600 - 7-M-l
Hours/Cost: Free (call voice phone for ID number)
B-3
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Networks
In order to join a network conference, you must have access to a computer system that is a node in that network.
Access to the network can then be made by subscribing to a LISTSERV or joining a newsgroup. Subscribing to a
LISTSERV is accomplished using the e-mail facility of a local node. A simple mail message is sent, SUB name, where
name is one of the address names below. Mail from that network conference will then appear in the user's e-mailbox.
Unsubscribing is accomplished by sending the message UNSUB name.
In addition, if the remote system permits, the user can access the remote node of the network via software like file
transfer protocol (FTP). Within a system like ftp, the user has direct access to the remote node as if it were a local
computer, and in some cases, software on the remote system can be run and the results later transferred to the local
node.
To FTP a remote site, the user types ftp node from the local node where node is one of the address names below. In
most cases, the remote node will require a login name and password if the ftp process is successful. The login name
is often anonymous and the password guest, although other login strings are often called for and can only be
determined by contacting the individual in charge of the remote system.
Name:
Network:
Purpose:
Access:
AQUIFER@BACSATA
BITNET
Discussion group on various ground-water protection issues.
LISTSERV
Expert Systems
Name:
Source:
System Requirements:
Cost:
Integrated Model Evaluation System
Environmental Protection Agency
Office of Solid Waste and Emergency Response
Versar, Inc.
Ecological Sciences and Analysis Division
9200 Runsey Road
Columbia, Maryland 21045
MSDOS
Not yet determined
Name:
Purpose:
Source:
Cost:
GMSYS
Estimate leach rates from landfills
ORD-BBS
Free
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APPENDIX C
SOLUTION METHODOLOGY
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APPENDIX C
Solution Methodology
Every ground-water model is based upon a set of
mathematical equations. Solution methodology refers
to the strategy and techniques used to solve these
equations. In ground-water modeling, the equations
are normally solved for head (water elevations in the
subsurface) and/or contaminant concentrations.
Mathematical methods developed to solve the ground-
water flow and transport equations can be broadly
classified as either deterministic or stochastic.
Deterministic methods assume that a system or process
operates such that the occurrence of a given set of
events leads to a uniquely definable outcome, while
stochastic methods presuppose the outcome to be
uncertain and are structured to account for this
uncertainty.
Most of the stochastic methods are not completely
stochastic in that they often utilize a deterministic
representation of soil processes and derive their
stochastic nature from their representation of inputs
and/or spatial variation of soil characteristics and
resulting chemical movement. While the deterministic
approach results in a specific value of a soil variable
(e.g., solute concentration) at pre-specified points in
the domain, the stochastic approach provides the
probability (within a level of confidence) of a specific
value occurring at any point.
The development of stochastic methods for solving
ground-water flow is a relatively recent endeavor that
has occurred as a result of the growing awareness of
the importance of intrinsic variability of the
hydrogeologic environment. Stochastic methods are
still primarily research tools; however, as computer
speeds continue to increase, stochastic methods will be
able to move further away from the research- oriented
community and more into mainstream management
applications. The more widespread use of
deterministic methods suggests a more immediate need
for code-selection guidance. Therefore, this section
focuses primarily on deterministic methods.
Deterministic methods may be broadly classified as
either analytical or numerical. Analytical methods
usually involve approximate or exact solutions to
simplified forms of the differential equations for water
movement and solute transport. Simple analytical
methods are based on the solution of applicable
differential equations which make a simplified
idealization of the field and give qualitative estimates
of the extent of contaminant transport. Such models
are simpler to use than numerical models and can
generally be solved with the aid of a calculator,
although computers are also used. Analytical models
are restricted to simplified representations of the
physical situations and generally require only limited
site-specific input data. They are useful for screening
sites and scoping the problem to determine data needs
or the applicability of more detailed numerical models.
Analytical models are used in ground-water
investigations to solve many different kinds of
problems. For example, aquifer parameters are
obtained from aquifer tests through the use of
analytical models, and ground-water flow and
contaminant transport rates can also be estimated with
the use of analytical models. To avoid confusion, only
analytical models designed to estimate ground-water
flow and radionuclide transport rates are discussed in
this section.
Numerical models provide solutions to the differential
equations describing water movement and solute
transport using numerical methods such as finite
differences and finite elements. Numerical methods
can account for complex geometry and heterogenous
media, as well as dispersion, diffusion, and chemical
retardation processes (e.g., sorption, precipitation,
radioactive decay, ion exchange, degradation). These
methods always require a digital computer, greater
quantities of data than analytical modeling, and an
experienced modeler-hydrogeologist.
The validity of the results from numerical models
depends strongly on the quality and quantity of the
input data. Numerical and analytical codes have their
respective strengths and weaknesses which are
inherent within their formulations. The fundamental
characteristics of both analytical and numerical
methods are presented below and are discussed in more
detail in the following sections:
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Analytical
Analytical Methods
! Provides a solution at any location and point
in time;
! Exact, closed-form solutions or well-
documented, convergent solutions
(approximate analytical);
! Requires regular geometry of the domain;
! Generally requires uniform material
properties;
! 1-, 2-, or 3-D capability;
! Transient effects can be considered;
! Less prone to computational errors than
numerical methods;
! Usually requires that problems are linear;
! Low computer storage requirements;
! Data can be easily input.
Numerical
! Provides a solution only at prespecified
locations and moments in time;
! Approximate solutions;
! Irregular domain and boundaries can be
simulated;
! Nonuniform material properties can be
simulated;
! Can simulate non-linear problems;
! 1-, 2-, or 3-D capability;
! Transient effects can be considered;
! Computational errors can be a problem;
! Can require large computer storage;
! Large amount of data input.
Analytical methods that solve ground-water flow and
contaminant transport in porous media are
comparatively easy to use. However, because the
governing equations are relatively simple, analytical
solutions are generally restricted to either radial flow
problems or to cases where velocity is uniform over the
area of interest. Except for some radial flow problems,
almost all available analytical solutions belong to
systems having a uniform and steady flow. This
means that the magnitude and direction of the velocity
throughout the system are invariable with respect to
time and space, which requires the system to be
homogeneous and isotropic with respect to the
hydraulic conductivity. The three most general types
of analytical methods include the following:
! Approximate analytical
! Exact analytical
! Semi-analytical
Typical analytical solutions, which are termed
approximate, are in the form of an infinite series of
algebraic terms, or a double infinite series, or even an
infinite series of definite integrals. Because an infinite
series of numbers cannot be solved for exact solutions,
each one of these expressions must be approximated by
truncating the series after considering a predetermined
number of terms. If, on the other hand, the analytical
solution can be expressed by equations which take a
closed form (finite number of terms), the solution is
said to be exact. Even though the solution may contain
errors due to rounding.
In general, exact analytical equations tend to require
infinite domains and boundaries. These constraints
typically result in solutions that are more appropriate
for solving problems of well hydraulics than those
associated with ground-water flow and contaminant
transport.
An obvious problem with approximate analytical
equations is that they are of an open form and may not
converge if they are inherently unstable. Therefore, it
is very important that care has been taken during the
code development process to ensure that the equations
used do converge properly and that the code
documentation provides the methods by which the
convergence was examined. It is also important to
C-3
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recognize that just because a code is written using
analytical techniques it does not mean that
convergence may not still be a problem even if the
formulation is correct.
Semi-analytical methods are more complex than
analytical methods and more simplistic than most
numerical methods. These techniques use the concepts
from fluid mechanics and velocity potentials which are
extended using numerical tools to construct flow and
contaminant patterns. Advantages of semi-analytical
methods include the following:
! Require only simple computer input data and
do not require the design of a mesh as with
fully numerical methods;
! May be used where complex boundaries (e.g.,
multiple pumping wells) do not allow
analytical equations to be written;
! Techniques can be used to easily estimate
travel times of a conservative, retarded, or
decaying contaminant to a downgradient
receptor;
! Can provide screening information to judge
the need for more sophisticated modeling.
Limitations of semi-analytical methods include the
following:
! Mass transport by dispersion and diffusion is
generally not considered, which in many
cases may lead to predictions of travel times
that are longer than actual values and may
underestimate the true impact of a
contaminant source;
! Usually are formulated in two dimensions and
three-dimensional effects are ignored;
! Heterogeneous properties of the media cannot
be simulated although some semi-analytical
methods do allow for anisotropy;
! Most semi-analytical formulations are for
steady-state problems; however, in some cases
they can be extended to handle transient
problems.
Numerical Methods
Unfortunately, the equations of flow and continuity in
the form of partial differential equations do not lend
themselves easily to rigorous analytical solutions when
boundaries are complex. Therefore, if a realistic
expression for hydraulic head or concentration as a
function of space cannot be written from the governing
equations, boundary and initial conditions, then
analytical methods are generally abandoned and more
approximate numerical methods are used to solve the
set of equations. The most common of these methods
include the following:
! Finite Difference
! Integrated Finite Difference
! Finite Element
! Method of Characteristics
Of particular importance to the following discussion is
the understanding that the flow and transport
equations, which describe the movement of ground
water and contaminants, are composed of both spatial
and temporal terms both of which require
discretization within the model domain. These terms
simply describe the concentration or head (i.e., water
elevations) in space and time. The numerical methods
mentioned above (i.e., finite element and finite
difference) are used as discretization methods for the
spatial term, whereas the time-stepping methods,
discussed later in this section, are used to discretize or
describe the temporal term.
Finite Difference
The basic idea of finite-difference methods is to
replace derivatives at a point by ratios of the changes
in appropriate variables over small but finite intervals.
Unlike analytical methods, where values can be
calculated at any point in the problem domain,
numerical methods (e.g., finite differences) make
approximations at a predetermined finite number of
points and reduce a continuous boundary-value
problem to a set of algebraic equations. Once the
partial differential equations have been converted into
a set of algebraic equations involving a number of
unknowns, the unknowns may be found by what are
termed matrix solvers.
In practice, the problem domain is divided into a
rectangular grid in which either the x and y
C-4
-------
intersections, called nodes, are designated as solution
points (i.e., mesh centered) or the solution points are
at the center of the grid cell (i.e., block centered).
Time step sizes are specified over the simulated time
of interest, and the mathematical expressions are
successively solved for each individual time step until
the solution converges upon a value which satisfies the
predesignated convergence criteria (i.e., error
tolerance).
The form of the system of equations is that the values
of head at each nodal point are a function of x and y
grid coordinates, as well as the size of specified time
steps. The values of head are related to the values in
the surrounding nodal points and those at the
beginning and at the end of a time step. If the values
at the beginning of a time step are known (which is
usually the case), the values at the end of the time step
are the unknowns, and the resulting system of
equations is a system of N linear equations with N
unknowns. The value N indicates the total number of
mesh points. Thus, the mathematical problem to be
solved is the solution of a linear system of equations.
The system of equations may turn out to be rather
large. For example, a grid with 50 mesh points in the
x-direction and 50 mesh points in the y-direction will
have 2,500 unknowns as well as equations to be
solved.
Relevant considerations related to the finite-difference
method include:
! Uses a direct Taylor Series approximation of
the derivative terms of the partial differential
equations at nodal points;
! Formulation is based on a rectangular (block-
centered or mesh-centered) grid;
! Relatively simple to formulate as compared to
other numerical methods;
! Conducive to efficient matrix solving
techniques;
! May be sensitive to grid orientation effects in
solving 2-D and 3-D flow and transport
problems;
! Use of rectangular grid necessitates staircase
(or stepwise) approximation of irregular
boundary and/or aquifer material zoning;
! May be prone to numerical dispersion or
oscillation in solving transport problems.
A closely related alternative to the conventional finite
difference is the integrated finite-difference method
which uses integral approximations of the partial
differential equations of nodal subdomains. The
primary advantage of this method is that it will
accommodate non-rectangular grid elements, which
allow irregular boundaries to be efficiently modeled.
The following, however, are the disadvantages
associated with this method:
! Necessitates more complex grid generation
scheme than the traditional finite-difference
method;
! Subdomain boundaries surrounding
individual nodes must satisfy certain
orthogonality constraints to ensure that mass
is conserved;
! Method leads to less efficient matrix solution
techniques than the conventional finite-
difference method.
ft^fl^ t .CMtJf U£rt"£rtlf»
Figure C. 1 Finite Two-Dimensional Elements
Finite Element
While approximations to a continuous solution are
defined at isolated points by finite differences, with
finite elements, the approximate solution (i.e., heads or
C-5
-------
concentration) is defined over the entire domain by
interpolation functions, although solutions to the
functions are calculated only at the element nodes.
This integral formulation for the governing ground-
water flow or solute transport equation leads to a
system of algebraic equations that can be solved for the
unknown(s) (i.e., hydraulic head, pressure head or
solute concentration) at each node in the mesh. The
method of weighted residuals is the commonly used
general approach that defines an approximate solution
to the boundary or initial value problem. When this
approximate solution is substituted into the governing
differential equation, an error or residual occurs at
each point (node) in the problem domain. The
weighted average of the residuals for each node in the
finite-element mesh is then forced to equal zero, thus
minimizing the error between the approxi-mate
solution and the actual solution. Relevant
characteristics of the finite-element method as
compared with the finite-difference method include:
! Allows a much greater flexibility in handling
irregular domain geometry, material
heterogeneity, and/or anisotropy;
! Less prone to numerical dispersion; however,
it is necessary to be more careful to limit
potential oscillation in solving the transport
problem;
! The elements do not have to be rectangular,
but can also be other simple polygons
(commonly triangles or quadrilaterals);
! Matrix solutions generally require
substantially greater computational effort and
computer storage capability;
! Finite-element solutions are less sensitive to
grid orientation.
Two typical problems that arise when solving the
contaminant transport equations are numerical
dispersion and artificial oscillation. Numerical
dispersion arises from grid size, time-step size, and the
fact that computers have a limited accuracy, thus some
of the round-off error will occur in computations. This
error results in the artificial spreading of contaminant
due to amplification of dispersivity. Hence, the
contaminant will disperse farther than it should with
a given physical, or "real" dispersivity. This extra
dispersion will result in lower peak concentrations and
more spreading of the contaminant. Methods exist to
control numerical dispersion, but the methods
themselves may introduce artificial oscillation.
Artificial oscillation is the over or undershooting of the
true solution by the model, and results in "waves" in
the solution. Usually numerical dispersion is
associated with the finite-difference method; however,
numerical oscillation is associated with the finite-
element method. Depending upon the method
employed to solve the advection term, both methods
can exhibit both types of behavior. Special techniques
have been developed to deal with these problems, one
of which is the Method of Characteristics (MOC).
This method has been widely used and can be applied
to finite differences as well as finite elements, in two or
three dimensions. The basic idea is to decouple the
advective part and the dispersive part of the transport
equation and to solve them successively. However, all
MOC methods are not strictly based on the principle of
mass conservation, hence large contaminant mass
balance errors may arise. While it is recognized that
these errors may be an artifact of the technique, the
quality of the results of a numerical model are judged,
in part, by the degree that mass is conserved.
Furthermore, the MOC technique requires much
longer run-times than finite-difference or finite-
element techniques.
----- r
Figure C-2. Three-Dimensional Elements
C-6
-------
Time Stepping
As mentioned previously, while finite-element and
finite-difference methods are used to approximate the
spatial terms of the transient flow and transport
equations, techniques are used to approximate the
temporal term. While there are several commonly
used variations of the finite-difference method, it is
beyond the scope of this discussion to elaborate on the
specifics for each of the techniques; what is important,
however, is an introduction to the technical terms and
a general understanding as to how the various methods
influence the model run-times as well as the results.
Four of the most common time-stepping schemes
include Explicit, Implicit, Mixed Explicit-Implicit, and
Alternating Direction Implicit Procedure.
Characteristics of each method are listed below.
Explicit:
! Numerical solution is conditionally stable.
! Often requires an excessive number of time
steps to simulate a practical problem.
! Due to numerical inefficiencies, method is
unsuitable for simulation of field problems
with a high degree of heterogeneity and/or
nonlinear flow conditions.
Implicit:
! Usually produces unconditionally stable
numerical solution for flow and transport.
! Much more flexible and robust than the
explicit time-stepping scheme.
! Matrix formulation and solution require
substantial computational effort (i.e.,
relatively long computer times are necessary
to model practical field problems).
Mixed Explicit-Implicit:
! Based on combined use of explicit and
implicit temporal approximations.
! Usually produces unconditionally stable
numerical solution for flow and transport.
! More robust than the explicit time-stepping
scheme, and generally more efficient than the
implicit scheme for ground-water flow and
transport solutions.
! Time-stepping scheme can be weighted in
favor of either method (i.e., explicit or
implicit) using a factor that ranges from 0 to
1. Weighting factors of 0, .5, and 1 result in
explicit, Crank-Nicholson, and fully implicit
formulations, respectively.
Alternating Direction Implicit Procedure:
! Usually produces unconditionally stable
numerical solution for flow and transport.
! Much more flexible and robust than the
explicit time-stepping scheme.
! May be prone to mass balance problems when
applied to field problems with high degree of
heterogeneity and/or nonlinear flow
conditions.
! Unsuitable for variably saturated flow
simulations.
I
Limited to rectangular finite-difference grids.
The end result of applying the time-stepping schemes
described above is that the flow and transport problem
is broken into multiple equations with multiple
unknowns for each pre-specified point in the model
domain (i.e., nodes). These multiple equa-tions will,
in turn, be solved through matrix algebra methods
which are discussed in a later section.
Linearization of Flow and Transport Equations
In earlier sections, several situations were presented in
which the equations describing ground-water flow and
contaminant transport are nonlinear. For transport
problems, the equations are nonlinear when changes in
concentration, pressure, and temperature cause
changes in viscosity, effective porosity, ordensity (e.g.,
multiphase fluid conditions). Nonlinearflow problems
involve those where the transmissivity is a function of
saturated thickness (i.e., water-table aquifers) or
hydraulic conductivity is a function of moisture content
(i.e., unsaturated zone).
C-7
-------
Under nonlinear flow and transport conditions each
node in the model domain has associated multiple
nonlinear equations. Priorto solving for the unknowns
of these equations through matrix algebra, an
intermediate step is required in which the equations
are linearized. Two of the most common procedures
used to perform this linearization are the Picard and
Newton-Raphson methods.
The Picard method:
! Is relatively simple to formulate as compared
to the Newton-Raphson procedure.
I
Generally produces a symmetric matrix for
the flow problem and thus requires
considerably less computer effort for the
matrix solution than the Newton-Raphson
method.
! May be prone to convergence difficulties for
highly nonlinear cases.
Qualities of the Newton-Raphson method include:
! Suitable for handling highly nonlinear cases.
! Generally requires substantially greater
computational effort for matrix formulation
and solution.
! Convergence of the procedure may depend on
continuity or smoothness of the nonlinear
functions.
As far as model selection is concerned, if it is expected
that the problem will be highly nonlinear, the code
selected should be able to apply the Newton-Raphson
method. It should also be recognized that in this
situation the calculations will take a relatively long
time for the computer to solve. Flow and transport
through the unsaturated zone become more nonlinear
as the contrast between ambient moisture content and
volume of recharge (e.g., rainfall) becomes more
pronounced. Therefore, the regional climate can
provide an indication as to whether unsaturated zone
flow and transport are likely to be nonlinear or highly
nonlinear. For example, high-intensity rainfall events
in the arid southwest would create very sharp contrasts
between the ambient moisture content and the
infiltrating pulse. Under these conditions, the code
would most likely need the Newton-Raphson
formulation. However, in areas of the humid
northeast, the ambient moisture contents are generally
high enough that the wetting front saturations are not
significantly different from the ambient moisture
content and therefore the nonlinear equations could be
adequately solved with the Picard method.
Matrix Solvers
As stated previously, following the spatial and
temporal discretization of the flow and transport
equations and in the case of nonlinear problems, the
linearization of the equations, it then becomes
necessary to solve the systems of multiple equations
with multiple unknowns. The most efficient means of
accomplishing this task is through matrix algebra.
Matrix equations can be solved by several means.
Some of the more common ones include:
! Direct Matrix Solution Techniques
! Iterative Alternating Direction Implicit
Procedure (IADIP)
! Successive Over-Relaxation Techniques
! Strong Implicit Procedure (SIP)
! Preconditioned Conjugate Gradient
(PCG)/Orthomin Techniques
It is important to recognize that matrix solving
techniques will rarely be the deciding factor in the
code selection process. However, some familiarity
with the capabilities of the matrix solvers will not only
provide a general recognition of the technical terms
but will also give some indication as to potential
hardware requirements. Therefore, the following
provides a superficial description of the various matrix
solvers listed above.
The following qualities are inherent in the Direct
Matrix Solution techniques:
! Produces highly accurate solution of the
matrix equation with minimal round-off
errors.
! Generally applicable to both finite-difference
and finite-element schemes.
-------
! Performs well for 2-D problems with up to
2,000 nodal unknowns; unsuitable for large
problems with many thousands of nodes.
Qualities of the Iterative Alternating Direction Implicit
Procedure (IADIP) include:
! Accommodates large 2-D and 3-D problems
with many thousands of nodal unknowns.
! Applicability limited to rectangular grids.
! Convergence rate is usually sensitive to grid
spacings and material heterogeneity and
anisotropy.
! Prone to asymptotic convergence behavior
and may require several hundreds or
thousands of iterations to reach satisfactory
convergence for a steady-state analysis.
Qualities inherent in Successive Over-Relaxation
Techniques (i.e., Point Successive Over-Relaxation
(PSOR), Line Successive Over-Relaxation (LSOR),
and Slice Successive Over-Relaxation (SSOR))
include:
! Convergence rate is sensitive to iteration
parameter and grid spacings.
! Applicable to finite-difference approximation
and flow problems only.
Qualities inherent in the Preconditioned Conjugate
Gradient (PCG)/Orthomin Techniques include:
! Accommodates large 2-D and 3-D problems
with many thousands of nodal unknowns.
! No relaxation factor or iteration parameters
are required and convergence rate is usually
insensitive to grid spacings and material
anisotropy and/or heterogeneity.
! Much more robust than other alternative
iteration techniques.
I
Applicable to both finite-difference and
finite-element approximation schemes but
requires substantially less storage and
computer (CPU) time with finite-difference
approximation, particularly for 3 -D problems.
! Accommodates large 2-D and 3-D problems
with many thousand nodal unknowns.
! Applicable to finite-difference and finite-
element approximation schemes.
! Convergence rate is dependent on the choice
of relaxation factors and is usually sensitive
to grid spacings and material heterogeneities
and anisotropies.
! Prone to asymptotic convergence behavior
and may require several hundreds or
thousands of iterations to reach satisfactory
convergence for a steady-state analysis.
Qualities inherent in the Strong Implicit Procedure
(SIP) include:
! Accommodates large 2-D and 3-D problems
with many thousand nodal unknowns.
! Much more robust than IADIP and
PSOR/LSOR/SSOR techniques.
C-9
-------
APPENDIX D
CODE ATTRIBUTE TABLES
D-l
-------
Site-Related Features of Ground Water Flow and Transport Codes
COMPUTER CODE
BOUNDARY/SOURCE
CHARACTERISTICS
| POINT SOURCE |
| LINE SOURCE |
| AREALLY DISTRIBUTED |
| SPECIFIED |
| SPECIFIED SOURCE RATE |
| TIME-DEPENDENT |
| MULTIPLE SOURCES |
AQUIFER SYSTEM
CHARACTERISTICS
| CONFINED AQUIFERS |
| AQUITARDS |
| WATER-TABLE |
| CONVERTIBLE AQUIFERS |
| MULTIPLE AQUIFERS |
SOIL/ROCK CHARACTERISTICS
| HOMOGENEOUS |
| HETEROGENEOUS |
| ISOTROPIC |
| ANISOTROPIC |
| FRACTURED |
| MACROPORES |
| LAYERED SOILS |
REFERENCE
CITATION
COMPUTER
CODE
TRANSPORT & FATE PROCESSES
-
DISPERSION
-
ADVECTION
-
MATRIX DIFFUSION
DENSITY-DEPENDENT
-
RETARDATION
-
NON-LIN. SORPTION
CHEMICAL REACTIONS/
SINGLE SPECIES
1 MULTI-SPECIES TRANS-
PORT WITH CHAINED
MULTIPHASE
FLUID CONDITIONS
TWO-PHASE
| TWO-PHASE WATER/AIR
1 THREE-PHASE WATER/
NAPL/AIR
FLOW
CONDITION^^
| FULLY SATURATED
VARIABLY SATURATED/
NON-HYSTERETIC
VARIABLY SATURATED/
TIME
DEPENDENCE
| STEADY-STATE
| TRANSIENT
-------
Code-Related Features of Ground Water Flow and Transport Codes
COMPUTER CODE
SOLUTION METHODOLOGY
APPROX. ANALYTICAL _ | ;>
1 g.
EXACT ANALYTICAL | ^.
SEMI-ANALYTICAL |
Numerical
FINITE DIFFERENCE |£
INTEGRATED FINITE- &
K2
1 *4
| FINITE ELEMENT ||
iOfc
METHOD OF CHARAC.
sen zati
EXPLICIT
IMPLICIT
MIXED IMPLICIT-
Mateg Solars
PH
3
DIRECT SOLUTION
ITERATIVE ADIP
SOR/LSOR/SSOR
P_H
GO
PCG/ORTHOMIN
GEOMETRY
Q
2-D CROSS SECTIONAL
2-DAREAL
QUASI 3-D (LAYERED)
| FULLY 3-D
COMPUTER CODE
OTHER RELEVANT FACTORS
Source Code
^ailabili^
| PROPRIETARY
| NON-PROPRIETARY
Code Testing and
Pess
| VERIFIED
| FIELD-VALIDATED
| PC- VERSION 386-SR486
| PRE AND POST
_
(CONTAMINANT MASS/
RATE OF RELEASE TO
GROUNDWATER FROM
CONTAMINANT PLUME 1
EXTENT |
(CONTAMINANT 1
CONCENTRATION ASA 1
FUNCTION OF DISTANCE 1
ii r*,
AS A FUNCTION OF 1 *f
CONTINUOUSLY 1
DISTRIBUTED IN SPACE |
_
(CONTAMINATION
AVERAGE
AT SELECTED POINTS
PROFILES AT SELECTED
POINTS OVER TIME
-------
APPENDIX E
INDEX
E-l
-------
INDEX
D
Adsorption S-12, 3-3, 4-35, 4-37, 4-51, A-2, A-6
Advection S-9, S-12, S-13, S-16, 4-20, 4-25, 4-35,
4-37, 4-38, 4-39, 4-40, 4-45, 5-4, 5-20, A-2, C-6,
D-3
Alluvial flood plane 4-15
Analytical model 4-7, A-2
Anion exclusion 4-17, 4-41, A-2
Anisotropic S-7, S-9, S-10, S-ll, 4-2, 4-9, 4-25,
4-28, 4-32, 5-7, A-2, D-3
Aquifer S-5, S-8, S-9, S-10, S-ll, S-12, S-16,
1-3, 1-4, 3-5, 4-4, 4-9, 4-10, 4-12, 4-13, 4-16,
4-18, 4-22, 4-24, 4-25, 4-27, 4-28, 4-29, 4-30,
4-35, 4-36, 4-37, 4-38, 4-39, 4-45, 4-46, 4-47,
4-49, 5-4, 5-8, 5-16, 5-20, 5-22, A-2, A-3, A-4,
A-5, A-6, B-4, C-2, C-5, D-l
Aquitards S-10, S-ll, S-16, 4-10, 4-22, 4-28, 4-30,
4-37, 4-45, 4-46, 5-4, 5-20, 5-22, D-2
Artesian well A-2
B
Basalt 3-4, A-2
Bedrock 4-15, A-2
Benchmark S-15, 5-1, 5-2
Biofixation 4-17, 4-18, 4-41, A-2
Bulk density A-2
Calibration 4-12, 4-16, 4-31, 4-32, 4-40, 4-47, A-2
Capture zone S-13, 4-40, 4-43, A-2
Chain decay S-17, 5-5, A-3
Channeling 4-37
Chemisorption S-13, 4-41
Clay S-13, 4-16, 4-17, 4-49, A-3, A-4, A-6
Complexation 3-3, 4-16, 4-17, 4-50, A-5
Concentration gradient S-13, 4-40
Conceptual model S-l, S-5, S-6, S-8, S-12, 1-3,
1-4, 1-5, 3-1, 3-2, 3-3, 3-5, 4-1, 4-3, 4-6,
4-7, 4-10, 4-11, 4-12, 4-14, 4-21, 4-24, 4-31,
4-32, 4-39, 4-47, 5-8, 5-15, 5-16
Convergence 4-15, 4-34, C-4, C-5, C-8, C-9
Curvilinear elements 4-37, A-3
Darcy's Law 4-30, 4-49, A-2, A-3
Deterministic model 4-47, 5-15, A-3
Dip 4-31, 4-36, A-3
Discharge 3-4, 3-5, 4-13, 4-31, 4-32, 4-43, 4-49,
A-3
Dispersion S-6, S-9, S-10, S-12, S-13, S-16, 1-2,
3-5, 4-13, 4-17, 4-20, 4-25, 4-27, 4-28, 4-32,
4-35, 4-37, 4-38, 4-39, 4-40, 4-45, 5-4, 5-16,
5-20, A-3, A-4, A-5, C-2, C-4, C-5, C-6, D-3
Distribution coefficient S-13, S-14, 2-2, 4-9, 4-15,
4-41, 4-42, 4-50, 5-8, A-3
Downgradient S-2, S-3, 1-3, 2-1, 2-4, 3-5, 4-5,
4-11, 4-12, 4-13, 4-19, 4-27, 4-43, 4-45, 5-20,
C-4
E
Effective dose equivalent 2-6
Effective porosity 4-4, 4-30, A-3, C-7
Equilibrium isotherm S-17, 5-5
Exposure scenarios S-4, S-5, S-6, 2-4
Facilitative transport 4-5, 4-15, 4-48, 4-49, A-3
Fault 4-50, A-3
Finite difference 4-26, A-3, A-5, C-4, C-5, D-5
Finite element 4-26, A-3, A-5, C-4, C-6, D-5
Flocculation 4-16, A-3
Fractured lithology A-3
Freundlich isotherm A-3
Geochemical facies 4-15, A-4
E-2
-------
H
M
Hydraulic gradient S-13, 4-4, 4-17, 4-40, 4-49, A-4
Hydrodynamic dispersion S-12, S-13, 4-35, 4-37,
4-39, A-4
Hydrofracturing 4-17, A-4
Hydrogeologic unit 4-50
Hydro statigraphic unit A-4
Hysteresis 4-44, A-4
I
Immiscible S-14, 4-42, A-4, A-5
In-situ coating 4-16
In-situ freezing 4-16
Institutional control S-4, 2-4
Integrated finite difference A-5, C-4
Intrinsic permeability S-ll, 4-32, A-4
Inverse model A-4
Ion exchange S-13, 4-18, 4-41, 4-49, 5-16, A-4, C-2
Ionic or molecular constituents S-13, 4-40, A-5
Macropores S-9, S-10, S-ll, S-16, 4-5, 4-9, 4-15,
4-22, 4-25, 4-28, 4-32, 4-33, 4-34, 4-35, 4-44,
5-4, A-5, D-3
Matrix diffusion S-9, S-12, S-13, 4-14, 4-15, 4-18,
4-20, 4-22, 4-25, 4-38, 4-39, 4-40, A-5, D-3
Mechanical dispersion S-13, 4-39
Metamorphic rock 4-36, A-5
Model S-l, S-2, S-5, S-6, S-7, S-8, S-10, S-ll,
S-12, S-13, S-14, S-15, S-16, S-18, S-19, S-20,
1-2, 1-3, 1-4, 1-5, 2-7, 2-8, 3-1, 3-2, 3-3, 3-5,
4-1, 4.3, 4.4, 4.5, 4-6, 4-7, 4-9, 4-10, 4-11, 4-12,
4-13, 4-14, 4-15, 4-16, 4-20, 4-21, 4-22, 4-23,
4-24, 4-26, 4-27, 4-28, 4-30, 4-31, 4-32, 4-37,
4-38, 4-39, 4-40, 4-42, 4-43, 4-44, 4-45, 4-47,
4-48, 4-50, 4-51, 5-1, 5-2, 5-4, 5-5, 5-7, 5-8,
5-10, 5-13, 5-14, 5-15, 5-16, 5-20, A-2, A-3, A-4,
A-5, B-2, B-4, C-2, C-4, C-6, C-7, C-8
Molecular diffusion S-13, 4-35, 4-39, A-5
Monitor wells S-4
Multiple aquifers S-9, S-10, S-ll, S-16, 4-16, 4-22,
4-25, 4-28, 4-30, 5-4, D-2
Joint sets 4-36
K
Kinetic activity 4-40, A-5
Langmuir isotherm A-4
Layered lithology A-4
Leach 1-3, 4-20, A-5, B-4
Leachate S-2, S-10, 1-4, 2-1, 2-2, 4-28, 4-43, A-5
Limestone 3-4, 4-36, 4-49, A-5
Lithography 3-2, 4-7
Littoral A-5
Loading rates 4-43, A-5
Low permeability barriers S-12, 4-38, A-5
N
Numerical model 4-9, 4-11, 4-47, A-5, C-6
Numerical oscillations S-12, 4-39
O
Off-centerline dispersion modeling 3-5
One-dimensional S-8, 3-4, 4-2, 4-5, 4-6, 4-27, 4-45,
5-20
Organic Complexation 4-17, A-5
Oxidation-reduction potential 4-16
Particle track A-5
Partition factors S-2, 2-2
Perched water 4-32, A-5
Porous media S-12, 3-5, 4-4, 4-9, 4-14, 4-35, 4-36,
4.39, 4.44, 5.7, A-3, A-5, A-6, C-3
Pyrophoric 4-31
E-3
-------
R
Radial flow 4-9, A-6, C-3
Radioactive decay S-ll, S-12, S-14, S-17, 3-3,
4-12, 4-28, 4-37, 4-38, 4-41, 4-42, 5-5, 5-16, A-3,
A-6, C-2
Receptors S-5, S-6, 1-4, 2-6, 3-2, 3-5, 4-4, 4-5,
4-11,4-12,4-19,4-27
Recharge 3-4, 3-5, 4-4, 4-5, 4-9, 4-13, 4-18, 4-19,
4-20, 4-28, 4-29, 4-30, 4-31, 4-33, 4-34, 4-35,
5-7, 5-22, A-6, C-8
Regional scale 3-4, 3-5
Remediation S-l, S-2, S-4, S-7, S-12, S-13, S-16,
1-2, 1-3, 1-5, 2-1, 2-3, 2-6, 2-7, 3-1, 3-2, 4-1,
4-2, 4-3, 4-7, 4-11, 4-21, 4-29, 4-30, 4-32, 4-38,
4-40, 4-43, 5-4, 5-7
Retardation factor/coefficient A-6
Sandstone S-ll, 4-9, 4-36, 4-37, A-6
Saturated zone S-ll, 3-4, 4-5, 4-6, 4-7, 4-10, 4-12,
4-13, 4-19, 4-30, 4-31, 4-34, 4-35, 4-43, 4-44,
4-48, 5-8, 5-20, A-6
Secondary mineralization 4-16
Sedimentary environment A-6
Shale 3-4, A-6
Silt A-6
Solute S-12, S-13, 4-33, 4-37, 4-38, 4-39, 4-41,
4-42, 4-47, 4-48, 5-8, 5-16, 5-20, A-2, A-3, A-4,
C-2, C-6
Solution features 4-15, A-6
Source term S-5, S-10, 3-2, 3-3, 4-12, 4-18, 4-24,
4-27, 4-28, 4-43, 4-44, 4-45, 4-48, 4-50, 5-20,
A-6
Speciation S-9, S-17, 4-17, 4-25, 4-41, 4-49, 5-5,
A-6, D-4
Three-dimensional S-8, 4-1, 4-7, 4-12, 4-13, 4-15,
4-19, 4-27, 4-45, 4-46, 5-20, 5-22, C-4, C-6
Two-dimensional 4-2, 4-5, 4-6, 4-12, 4-13, 4-19,
4.45, 4-46, 4-48, 5-16, 5-20, 5-22, C-5
E-4
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